Questions: Simplify. Express your answer as the given base raised to a single exponent. (4^(-3))^(-5)

Solution Steps

To simplify the expression \((4^{-3})^{-5}\), we can use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). Applying this property will allow us to combine the exponents into a single exponent.

To simplify the expression \((4^{-3})^{-5}\), we use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). Applying this property, we have:

\[ (4^{-3})^{-5} = 4^{-3 \cdot (-5)} = 4^{15} \]

Now, we calculate \(4^{15}\). This is a straightforward computation:

\[ 4^{15} = 1073741824 \]

Final Answer