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Mila [183]
3 years ago
10

(64/125) to the power of -2/3

Mathematics
1 answer:
Sedaia [141]3 years ago
7 0
As the exponent is negative, we can rewrite the expression as (125/64) raised to the power 2/3.

So, (125/64) raised to the power 2/3 can also be written as [(5/4) raised to the power 3] raised to the power 2/3. The exponents will multiply and the final exponent will be 2.

Hence the answer will be (5/4) squared.
Therefore the answer is (24/16).
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3 years ago
Find the average rate of change of f(x)=2x-1 from x=-1 to x=2
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The average rate of change from x = -1 to x = 2 is 2

<u>Solution:</u>

Given function is:

f(x) = 2x - 1

We have to find the average rate of change from x = -1 to x = 2

<em><u>The average rate of change is given as:</u></em>

\text {Average rate of change}=\frac{f(b)-f(a)}{b-a}

<em><u>The average rate of change from x = -1 to x = 2 is given by formula:</u></em>

\text {Average rate of change}=\frac{f(2)-f(-1)}{2-(-1)}\\\\\text {Average rate of change}=\frac{f(2)-f(-1)}{3}

<em><u>Find f(2) and f( - 1)</u></em>

<em><u>Substitute x = 2 in given function</u></em>

f(2) = 2(2) - 1 = 4 - 1 = 3

<em><u>Substitute x = -1 in given function</u></em>

f( - 1) = 2(-1) - 1 = -2 - 1 = -3

<em><u>Substitute the values in above formula,</u></em>

\text {Average rate of change}=\frac{3-(-3)}{3}=\frac{6}{3}=2

Thus average rate of change from x = -1 to x = 2 is 2

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Read 2 more answers
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