Identify Base and Exponents: Identify the base and the exponents in the expression (5^2)^-3. The base is 5 and it has two exponents: 2 and -3.Apply Power of Power Rule: Apply the power of a power rule which states that (a^m)^n = a^(m*n). Calculate the new exponent by multiplying the exponents 2 and -3 together. New exponent = 2 * -3 = -6.Calculate New Exponent: Rewrite the expression with the new exponent: 5^-6. This means 1 divided by 5^6.Rewrite Expression with New Exponent: Calculate 5^6 to find the denominator. 5^6 = 5 * 5 * 5 * 5 * 5 * 5 = 15625.Calculate Denominator: Now, divide 1 by 15625 to get the final answer. Final answer = 1 / 15625.

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$(5^2)^{-3}$

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(5^2)^{-3}

Identify Base and Exponents: Identify the base and the exponents in the expression $(5^2)^{-3}$ . The base is $5$ and it has two exponents: $2$ and $-3$ .
Apply Power of Power Rule: Apply the power of a power rule which states that a^m)^n = a^{(m*n)}\.$\newlineCalculate the new exponent by multiplying the exponents \$2$ and (-3\)\ together.$\newline$New exponent = $2 * -3 = -6$.
Calculate New Exponent: Rewrite the expression with the new exponent: $5^{-6}$. This means $1$ divided by $5^6$.
Rewrite Expression with New Exponent: Calculate $5^6$ to find the denominator.$\newline$$5^6 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 15625$.
Calculate Denominator: Now, divide $1$ by $15625$ to get the final answer.$\newline$Final answer = $\frac{1}{15625}$.