Question

step 3: apply the power of a power rule.
(2³)⁵ = 2¹⁵

Explanation:

Step1: Recall the power of a power rule

The power of a power rule states that \((a^m)^n = a^{m\times n}\), where \(a\) is the base and \(m,n\) are exponents.

Step2: Apply the rule to \((2^{3})^{5}\)

Here, \(a = 2\), \(m = 3\), and \(n = 5\). Using the power of a power rule, we multiply the exponents: \(3\times5 = 15\). So \((2^{3})^{5}=2^{3\times5}=2^{15}\).

Answer:

The simplification of \((2^{3})^{5}\) using the power of a power rule is \(2^{15}\), and the given equation \((2^{3})^{5}=2^{15}\) is correct.