Answers
Answer:
1/6^3
Step-by-step explanation:
The applicable rules of exponents are ...
a^-b = 1/a^b
(a^b)(a^c) = a^(b+c)
__
Your expression can be simplified as follows:
[tex]\dfrac{6^{-5}}{6^{-2}}=\dfrac{1}{(6^{-2})(6^5)}=\dfrac{1}{6^{-2+5}}=\boxed{\dfrac{1}{6^3}}[/tex]
_____
Additional comment
If you think of an exponent as signifying repeated multiplication, the rules of exponents may be easier to remember. The exponent tells you how many times the base is a factor in the product.
Consider multiplication:
[tex](x\cdot x\cdot x)\cdot(x\cdot x)=x^3\cdot x^2=x^{3+2}=x^5\\\\(x\cdot x\cdot x)\cdot(x\cdot x\cdot x)=(x^3)^2=x^{3\cdot2}=x^6[/tex]
Consider division:
[tex]\dfrac{x\cdot x\cdot x}{x\cdot x}=x\quad\Longleftrightarrow\quad\dfrac{x^3}{x^2}=x^{3-2}=x^1\\\\\dfrac{x\cdot x}{x\cdot x\cdot x}=\dfrac{1}{x}\quad\Longleftrightarrow\quad\dfrac{x^2}{x^3}=x^{2-3}=x^{-1}[/tex]
This may help you see that a positive exponent in the denominator is equivalent to a negative exponent in the numerator (and vice versa).
Related Questions
#7 What is f(4) if f(1) = 3.2 and f(x + 1) = 2.5f(x)?
Answers
========================================================
Explanation:
We're given f(1) = 3.2 which says the first term of the sequence is 3.2
To find the second term, we use the other equation, which is the recursive equation. Plug in x = 1 to get...
f(x+1) = 2.5*f(x)
f(1+1) = 2.5*f(1)
f(2) = 2.5*f(1)
f(2) = 2.5*3.2
f(2) = 8
The second term is 8. We multiplied the previous term (3.2) by the factor 2.5 to get this second term.
The third term is handled pretty much in a similar fashion
third term = 2.5*(second term)
third term = 2.5*8
third term = 20
Lastly, the fourth term f(4) is...
f(x+1) = 2.5*f(x)
f(3+1) = 2.5*f(3)
f(4) = 2.5*f(3)
f(4) = 2.5*20
f(4) = 50
The fourth term is 50.
The first four terms are: 3.2, 8, 20, 50
1. A vendor at the farmer's market was selling a bag of 8 potatoes for $2.56. Another
vendor was selling a bag of 10 potatoes for $4.32. Which bag is the better deal?
Answers
Answer:
The second bag is the better deal
Step-by-step explanation:
8÷2.56= $3.13 per potato
10÷ 4.32= $2.31 per potato
Mitch is attending a 4-year college. As a freshman, he was approved for a 10-year, federal
unsubsidized student loan in the amount of $8,100 at an APR of 4.29%. Mitch decides to
make no payments during the 4.5-year deferment period. After interest is capitalized at the
end of the 4.5-year period, what will his new principal amount be?
Answers
Answer:
Interest capitalization occurs when unpaid interest is added to the principal amount of your student loan. When the interest on your federal student loan is not paid as it accrues (during periods when you are responsible for paying the interest), your lender may capitalize the unpaid interest.
Step-by-step explanation:
Darren got 42 out of 56 questions correct on a test. What percent of the questions did he get correct?
Answers
Answer:
75%
42/56 = 42/56
Convert to decimal form:
42÷56 = 0.75
= 75%
Can you mark as brainliest if its right?
Answer:
75%
Step-by-step explanation:
42/56 = 0.75 = 75%
Brienne stated that 0.33 and
1/3 are equivalent. Do you agree? Explain why or why
not.
Answers
Answer:
it is not
Step-by-step explanation:
0.33 is rounded off whereas 1/3 would have a continued decimal of 3, i.e. 0.333333333
Jarrod earns $12 an hour at his job. The table shows what Dale earns at his job. Which statement is true?
Answers
Answer:
Need the table, and the statements
Step-by-step explanation:
It takes 2 yards of material to
make 6 scarves, how many yards of material are needed to make 24
scarves?
Answers
Hope this helped
What is the solution to 0. 3(12x - 16) = 0. 4(12 - 3x)?.
Answers
Answer:
[tex]x = 2[/tex]
Step-by-step explanation:
[tex]3\left(12x-16\right)=4\left(12-3x\right)[/tex]
First, let's solve the brackets. Use the distribution property. It simply means multiplying the value outside of the brackets to each value inside the brackets.
[tex]3\left(12x-16\right)[/tex]
[tex]=3\cdot \:12x-3\cdot \:16[/tex]
[tex]=36x-48[/tex]
[tex]4\left(12-3x\right)[/tex]
[tex]=4\cdot \:12-4\cdot \:3x[/tex]
[tex]=48-12x[/tex]
Now we've simplified the expression to:
[tex]36x-48=48-12x[/tex]
[tex]\mathrm{Add\:}48\mathrm{\:to\:both\:sides}[/tex]
[tex]36x-48+48=48-12x+48[/tex]
[tex]36x=-12x+96[/tex]
[tex]\mathrm{Add\:}12x\mathrm{\:to\:both\:sides}[/tex]
[tex]36x+12x=-12x+96+12x[/tex]
[tex]48x=96[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}48[/tex]
[tex]\frac{48x}{48}=\frac{96}{48}[/tex]
[tex]\bold{x=2}[/tex]
Therefore, the answer is [tex]x = 2[/tex]
The solution of the given equation [tex]0. 3(12x - 16) = 0. 4(12 - 3x)[/tex] is [tex]x=2[/tex].
Given equation,[tex]0. 3(12x - 16) = 0. 4(12 - 3x)[/tex]
Use the simple rules of algebra like the BODMAS rule to get the equivalent expression for the given equation.
Simplified expression:Firstly, open the brackets and then multiply the coefficients. In the next step arrange the terms to get the simplified solution.
On Solving the brackets, we get
[tex]3.6x-4.8=4.8-1.2x\\[/tex]
[tex]3.6 \ x+1.2 \ x=4.8+4.8[/tex]
[tex]4.8 \ x=9.6 \\x=\dfrac{9.6}{4.8} \\[/tex]
[tex]\ x= 2[/tex]
Hence, the solution of the given equation is [tex]x=2[/tex].
For more details about expressions follow the link:
https://brainly.com/question/545403
Determine whether the given is a polynomial in one variable or not:
Polynomial: 4x^2-3x+7
Answers
The polynomial is
[tex] {4x}^{2} - 3x + 7[/tex]
Here all the exponents of x are whole numbers, i.e, 2 and 1 are whole numbers.So, this polynomial is a polynomial in one variable.Its variable is x.So, the given polynomial is a polynomial in one variable.
Hope you could get an idea from here.
Doubt clarification - use comment section.
Help help help help math
Answers
F(-1)= 3+3
F(-1)=6
please help me guys :) !
Answers
Answer:
{13, 9, 5, 1}
Step-by-step explanation:
Here the four inputs (x-values) are {1, 2, 3, 4}. The corresponding y-values are calculated using the formula y = 17 - 4x, and are as follows:
x y
1 17 - 4(1) = 13
2 17 - 4(2) = 9 In summary, the (vertical) 2nd column,
3 17 - 4(3) = 5 containing the y-values, is {13, 9, 5, 1}
4 17 - 4(4) = 1
SOS, I really need help! I accidentally slept in.
Answers
Dynamite blue fire red grape purple
find the derivative of sin2X
Answers
Step-by-step explanation:
Derivation using Product rule : -
To find the derivative of f(x) = sin 2x by the product rule, we have to express sin 2x as the product of two functions. Using the double angle formula of sin, sin 2x = 2 sin x cos x. Let us assume that u = 2 sin x and v = cos x. Then u' = 2 cos x and v' = -sin x. By product rule,
f '(x) = uv' + vu'
= (2 sin x) (- sin x) + (cos x) (2 cos x)
= 2 (cos2x - sin2x)
= 2 cos 2x
This is because, by the double angle formula of cos, cos 2x = cos2x - sin2x.
Thus, derivation of sin 2x has been found by using the product rule.
Answer:
2cos2x
Step-by-step explanation:
Using the Chain rule
[tex]\frac{d}{dx}[/tex] (sin2x)
= cos2x × [tex]\frac{d}{dx}[/tex] (2x)
= cos2x × 2
= 2cos2x
Simplify -1-18
-
(18)
O - |18|
0-18
O 18
Answers
Answer:
simplify -1-18
Step-by-step explanation:
Subtract 18 from −1
− 19
20 points.
The midpoint of AB is (-1, 5) and the coordinates of point A are (-3, 2) what are the coordinates of point B?
Answers
Answer:
B (1, 8 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
with (x₁, y₁ ) = A (- 3, 2 ) and (x₂, y₂ ) = B (x, y )
Calculate the midpoint values and equate to the corresponding coordinates of the given midpoint (- 1, 5 ) , that is
[tex]\frac{-3+x}{2}[/tex] = - 1 ( multiply both sides by 2 )
- 3 + x = - 2 ( add 3 to both sides )
x = 1
[tex]\frac{2+y}{2}[/tex] = 5 ( multiply both sides by 2 )
2 + y = 10 ( subtract 2 from both sides )
y = 8
Then point B = (1, 8 )
NEED HELP ASAP WILL GIVE BRAINLIESTfor which values of x does each expression make sense?sqrt x+5
Answers
Answer:
can I see a picture? so I can try & help u
Answer:
x≥-5
Step-by-step explanation:
How many solutions does 8 + x/6 = x/6 - 4 + 5x/12 have?
A. Two solutions.
B. No solutions
C. Infinitely many solutions
D.One solution
Answers
Answer:
It has got one solution since it is a linear equation which falls under polynomials
-3x-2y=-6
-3x+2y=18
(?,?)
Answers
[tex]\left \{ {-3x-2y = -6} \atop {-3x+2y=18} \right. <=>\left \{ {-6x=12} \atop {-3x+2y=18} \right. <=> \left \{ {x=-2} \atop {y=6} \right.[/tex]
The answer: ( x ; y ) = ( -2 ; 6 )
Ok done. Thank to me :>
is this correct ? if not what’s the correct answer?
Answers
It would be B. X is on a right angle which is 90 degrees and you must take into thinking that all three angles must be 180. Since it is a mirrored shape, corner E is the same as corner C which is 46.
This adds up to 136 and you must subtract 136 from 180 and is 44.
Simplify the expression.
53 + (- 12) + (- 4t)
Answers
Answer:
8
Step-by-step explanation:
41-4t
Hope this helps ^^
PLEASE HELP. WILL MAKE BRAINLIEST!!!!
1 cup of water with 1 1/2 teaspoons of powdered drink mix
2 cups of water with 1/2 teaspoon of powdered drink mix
1 cup of water with 1/4 teaspoon of powdered drink mix
Which of these recipes is for the stronger tasting mixture. Explain how you know.
Answers
Answer: 1 cup of water with 1 1/2 teaspoons of powdered drink.
Step-by-step explanation:
I know this, because if 1 cup is 1 1/2 teaspoons of powdered drink, then 2 cups of water would have 3 teaspoons of powdered drink mix, so the second option is out. And, the third option is out because it less than 1 cup of water with 1 1/2 teaspoons of powered drink mix.
Mr Thompson drew a rectangle on the chalk board with a length to width ratio 5 to 2 he asked students to draw a rectangle with the same ratio of length to width in their journals. Audrey plans to draw a rectangle with a width of 6 centimetres .
Answers
get ratioed skull skull
help me 20 pts pls and brainliest
Answers
Answer:
elaboration
Step-by-step explanation:
tthe definition of elaboration is the addition of more detail concerning what has already been said. so out of these options, elaboration best fits answers the question
To elaborate means to give more clarification about something
solve pls brainliest
Answers
Answer:
Yes
Yes
Yes
No
No
Step-by-step explanation:
-42/6 = -7
17/18 = 0.9444444 (4 repeating)
Integers = whole numbers whether negative or not, but it does not have a decimal.
For a given set of populations and house sizes, different methods of apportionment
may lead to different apportionments.
True
False
Answers
Answer: the answer should be true
solve using substitution
x-10y=10
x= -10
Answers
+10 +10
-10y = 20
20/-10 = -2
Y = -2
Answer:
y = -2Step-by-step explanation:
x - 10y = 10=> -10 - 10y = 10=> -10y = 10 + 10=> -10y = 20=> y = -2Conclusion:
Therefore, y = -2.
Hoped this helped.
[tex]GeniusUser[/tex]
NPM = __?__
Less than BAC
Less than CAB
Less than BCA
Less than ABC
Answers
By the way, the “less than” isn’t a less than symbol lol
Select the correct answer from each drop-down menu.
Answers
Answer:
so sorry i don't know the answer
can someone help me with this answer plsss
Answers
Answer: 44 ft
Step-by-step explanation:
if you add up the right square it adds up to 16 4+4+4+4 all sides are equal since its a square.
The left rectangle is
8+8=16
6+6=12
16+12=28
Now you add the square on the right to the square on the left which is
28+16= 44 ft
Simplify w4z8 ÷ w2y2z4.
Answers
Answer:
w^2z^4/y^2
Step-by-step explanation: