Question

if \\((2^x)^5=2^{15}\\), what does x equal?
\\(x = 3\\)
\\(x = 5\\)
\\(x = 10\\)

Explanation:

Step1: Apply exponent rule

Using the power of a power rule \((a^m)^n = a^{m\times n}\), for \((2^x)^5\), we get \(2^{x\times5}=2^{5x}\).

Step2: Set exponents equal

Since the bases are the same (\(2\)), we set the exponents equal: \(5x = 15\).

Step3: Solve for x

Divide both sides by \(5\): \(x=\frac{15}{5}=3\).

Answer:

\(x = 3\) (corresponding to the option with \(x = 3\))