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Find the value of
64^(-(2)/(3))
(1 mark)

theta
◻
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Find the value of $64^{-\frac{2}{3}}$ $\newline$ ( $1$ mark) $\newline$ $\theta$ $\square$ $\newline$ Submit Answer

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Find trigonometric functions using a calculator

Full solution

Q. Find the value of

64^{-\frac{2}{3}}

\newline

(

1

mark)

\newline

\theta

\square

\newline

Submit Answer

Recognize Exponential Property: Recognize that $64^{-(2)/(3)}$ is the same as $(64^{-1})^{2/3}$ .
Calculate $64^{-1}$ : Calculate $64^{-1}$ , which is $\frac{1}{64}$ .
Find Cube Root of $\frac{1}{64}$ : Now take $(\frac{1}{64})^{\frac{2}{3}}$ . To do this, find the cube root of $\frac{1}{64}$ first, which is the same as the cube root of $1$ over the cube root of $64$ .
Calculate $(\frac{1}{64})^{\frac{2}{3}}$ : The cube root of $1$ is $1$ , and the cube root of $64$ is $4$ , so we have $\frac{1}{4}$ .
Raise $1$ / $4$ to Power: Now raise $1/4$ to the power of $2$ , which is $(1/4)^2$ .
Final Result: $(\frac{1}{4})^2$ is $\frac{1}{16}.$
Final Result: $(\frac{1}{4})^2$ is $\frac{1}{16}$ .So, $64^{-\left(\frac{2}{3}\right)}$ equals $\frac{1}{16}$ .

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