Which expression is equivalent to ((2)/(2^(5)))^(-1)? 16 32 64 (1)/(32)

Apply negative exponent rule: Understand the given expression and apply the negative exponent rule. The negative exponent rule states that a^(-n) = 1/(a^n). Therefore, ((2)/(2^(5)))^(-1) can be rewritten as 1/((2)/(2^(5))).Simplify expression inside parentheses: Simplify the expression inside the parentheses. Since 2^(5) is 2 multiplied by itself 5 times, we have 2^(5) = 2 * 2 * 2 * 2 * 2 = 32. So, the expression becomes 1/((2)/(32)).Simplify division inside parentheses: Simplify the division inside the parentheses. Dividing 2 by 32 gives us 1/16. So, the expression now is 1/(1/16).Invert fraction in denominator: Simplify the expression by inverting the fraction in the denominator. When you have a fraction in the denominator, you can invert it and multiply. So, 1/(1/16) becomes 1 * (16/1) which simplifies to 16.

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Q. Which expression is equivalent to

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

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16

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32

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64

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\frac{1}{32}

Apply negative exponent rule: Understand the given expression and apply the negative exponent rule. The negative exponent rule states that $a^{-n} = \frac{1}{a^n}$ . Therefore, $\left(\frac{2}{2^{5}}\right)^{-1}$ can be rewritten as $\frac{1}{\left(\frac{2}{2^{5}}\right)}$ .
Simplify expression inside parentheses: Simplify the expression inside the parentheses. $\newline$ Since $2^{5}$ is $2$ multiplied by itself $5$ times, we have $2^{5} = 2 \times 2 \times 2 \times 2 \times 2 = 32$ . So, the expression becomes $1/\left((2)/(32)\right)$ .
Simplify division inside parentheses: Simplify the division inside the parentheses. Dividing $2$ by $32$ gives us $\frac{1}{16}$ . So, the expression now is $\frac{1}{\frac{1}{16}}$ .
Invert fraction in the denominator: Simplify the expression by inverting the fraction in the denominator. $\newline$ When you have a fraction in the denominator, you can invert it and multiply. So, $1/(1/16)$ becomes $1 \times (16/1)$ which simplifies to $16$ .