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Simplify. Express your answer using a single exponent. $\newline$ $(11h^5)^2$

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Powers of a power: variable bases

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Q. Simplify. Express your answer using a single exponent.

\newline

(11h^5)^2

Apply Power to Base and Variable: Apply the power to both the base number and the variable with its exponent. When raising a power to a power, we multiply the exponents, and when raising a number to a power, we simply calculate the number to that power. $(11h^5)^2 = 11^2 \times (h^5)^2$
Calculate $11^2$ : Calculate $11^2$ . $\newline$ $11^2 = 11 \times 11 = 121$
Calculate $(h^5)^2$ : Calculate $(h^5)^2$ . When raising a power to another power, we multiply the exponents. $(h^5)^2 = h^{(5 \times 2)} = h^{10}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $121 \times h^{10}$

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