Question

what is the value of \\(\sqrt12{8^4}\\)?

enter your answer as a whole number, like this: 42

Explanation:

Step1: Rewrite the radical expression using rational exponents

$$\sqrt[12]{8^4} = (8^4)^{\frac{1}{12}}$$

Step2: Simplify the exponent product

$$8^{4 \times \frac{1}{12}} = 8^{\frac{1}{3}}$$

Step3: Express the base as a power of 2

$$(2^3)^{\frac{1}{3}}$$

Step4: Calculate the final value

$$2^{3 \times \frac{1}{3}} = 2^1 = 2$$

Answer:

2