Question

u5d1: rational exponents
score: 11/28 answered: 14/28
question 3
evaluate each expression (using exponent rules). no calculator.
$(2^8)^{\frac{1}{4}}$

Explanation:

Step1: Recall exponent rule

Use the power of a power rule: \((a^m)^n = a^{m \times n}\). Here, \(a = 2\), \(m = 8\), and \(n=\frac{1}{4}\).

Step2: Apply the rule

Multiply the exponents: \(8\times\frac{1}{4}=2\). So \((2^8)^{\frac{1}{4}} = 2^{8\times\frac{1}{4}}=2^2\).

Step3: Calculate \(2^2\)

\(2^2 = 4\).

Answer:

\(4\)