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Rewrite using a single positive exponent.

(5^(-6))^(6)

Rewrite using a single positive exponent. $\newline$ $\left(5^{-6}\right)^{6}$

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Roots of integers

Full solution

Q. Rewrite using a single positive exponent.

\newline

\left(5^{-6}\right)^{6}

Apply power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{(m*n)}$ . In this case, $a = 5$ , $m = -6$ , and $n = 6$ . $\newline$ So, $(5^{-6})^6 = 5^{(-6*6)}$ .
Multiply exponents: Multiply the exponents. $\newline$ $-6 \times 6 = -36$ . $\newline$ So, $5^{(-6\times6)} = 5^{-36}$ .
Convert to positive exponent: Convert the negative exponent to a positive exponent. $\newline$ A negative exponent indicates the reciprocal of the base raised to the positive of that exponent. Therefore, $5^{-36}$ can be rewritten as $1/(5^{36})$ .
Write final answer: Write the final answer. $\newline$ The expression $(5^{-6})^6$ is simplified to $\frac{1}{5^{36}}$ using a single positive exponent.

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