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Simplify. Express your answer using a single exponent. $\newline$ $(3t^8)^2$

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Powers of a power: variable bases

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

\newline

(3t^8)^2

Apply Power Rule: Apply the power of a power rule. $\newline$ To simplify the expression $(3t^8)^2$ , we need to apply the power of a power rule, which states that $(a^m)^n = a^{m*n}$ . We will apply this rule to both the coefficient $3$ and the variable $t$ with its exponent $8$ . $\newline$ $(3t^8)^2 = 3^2 \times (t^8)^2$
Calculate Coefficient Square: Calculate the square of the coefficient $3$ . We need to square the coefficient $3$ . $3^2 = 3 \times 3 = 9$
Apply Power Rule to Variable: Apply the power of a power rule to the variable $t$ with its exponent. $\newline$ Now we apply the power of a power rule to $t^8$ raised to the power of $2$ . $\newline$ $(t^8)^2 = t^{8*2} = t^{16}$
Combine Results: Combine the results to write the final simplified expression. $\newline$ We combine the squared coefficient and the variable with the new exponent to get the final simplified expression. $\newline$ $(3t^8)^2 = 3^2 \times t^{16} = 9t^{16}$

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