Questions: (5^(-2))^(-5)

Solution Steps

To solve the expression \((5^{-2})^{-5}\), we need to apply the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). In this case, we multiply the exponents \(-2\) and \(-5\).

To simplify the expression \((5^{-2})^{-5}\), we use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). Here, we have \(a = 5\), \(m = -2\), and \(n = -5\). Therefore, we calculate:

\[ (5^{-2})^{-5} = 5^{-2 \cdot (-5)} = 5^{10} \]

Now, we need to compute \(5^{10}\). This is done by multiplying 5 by itself 10 times:

\[ 5^{10} = 9765625 \]

Final Answer