Question

simplify.
$8^{\frac{4}{3}}$

Explanation:

Step1: Rewrite 8 as a power of 2

Since \( 8 = 2^3 \), we can rewrite the expression \( 8^{\frac{4}{3}} \) as \( (2^3)^{\frac{4}{3}} \).

Step2: Apply the power - of - a - power rule \((a^m)^n=a^{m\times n}\)

Using the rule \((a^m)^n = a^{m\times n}\), where \(a = 2\), \(m = 3\) and \(n=\frac{4}{3}\), we have \((2^3)^{\frac{4}{3}}=2^{3\times\frac{4}{3}}\).

Step3: Simplify the exponent

Simplify the exponent \(3\times\frac{4}{3}\). The 3 in the numerator and the 3 in the denominator cancel out, leaving us with \(2^4\).

Step4: Calculate \(2^4\)

We know that \(2^4=2\times2\times2\times2 = 16\).

Answer:

\(16\)