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

Transcript text: $\left(5^{-2}\right)^{-5}$

Solution

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 $-5$.

Step 1: Apply the Power of a Power Property

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:

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

Step 2: Calculate the Result

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

\[ 5^{10} = 9765625 \]