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Simplify. Express your answer using a single exponent. $\newline$ $(3s^7)^4$

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Powers of a power: variable bases

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

\newline

(3s^7)^4

Apply Power Rule: Apply the power of a power rule to the expression $(3s^7)^4$ . The power of a power rule states that when raising a power to another power, you multiply the exponents. In this case, we have an exponent outside the parentheses that needs to be distributed to both the coefficient $3$ and the variable $s$ raised to the $7$ th power. $(3s^7)^4 = 3^4 \times (s^7)^4$
Calculate $3^4$ : Calculate $3^4$ . $\newline$ $3^4$ means $3$ multiplied by itself $4$ times. $\newline$ $3^4 = 3 \times 3 \times 3 \times 3 = 81$
Calculate $(s^7)^4$ : Calculate $(s^7)^4$ . Using the power of a power rule, we multiply the exponents $7$ and $4$ . $(s^7)^4 = s^{(7 \times 4)} = s^{28}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ Now we have the coefficient raised to the $4^{\text{th}}$ power and the variable raised to the $28^{\text{th}}$ power. We combine these to express the answer using a single exponent. $\newline$ $(3s^7)^4 = 3^4 \times s^{28} = 81s^{28}$

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