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20 (1 point)
of the expression
(((2^(-3))(2^(5)))/(2^(8)))^(-(1)/(3)) is
age
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$20$ ( $1$ point) $\newline$ of the expression $\left(\frac{\left(2^{-3}\right)\left(2^{5}\right)}{2^{8}}\right)^{-\frac{1}{3}}$ is $\newline$ age $\newline$ Next Page

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Operations with rational exponents

Full solution

Q.

20

(

1

point)

\newline

of the expression

\left(\frac{\left(2^{-3}\right)\left(2^{5}\right)}{2^{8}}\right)^{-\frac{1}{3}}

is

\newline

age

\newline

Next Page

Combine Powers of $2$ : Combine the powers of $2$ in the numerator using the property $a^m \cdot a^n = a^{m+n}$ . $(2^{-3}) \cdot (2^{5}) = 2^{-3+5} = 2^{2}$ .
Divide by $2^8$ : Now divide the result by $2^8$ using the property $a^m / a^n = a^{m-n}$ . $\newline$ $2^{2} / 2^{8} = 2^{2-8} = 2^{-6}$ .
Raise to Power of $-1$ / $3$ : Raise the result to the power of $-\frac{1}{3}$ using the property $(a^m)^{(n)} = a^{(m*n)}$ . $\newline$ $(2^{-6})^{-(\frac{1}{3})} = 2^{-6 * -(\frac{1}{3})} = 2^{\frac{6}{3}} = 2^{2}$ .
Simplify $2^2$ : Simplify $2^{2}$ . $2^{2} = 2 \times 2 = 4$ .

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