Question

the expression \\(sqrt3{64a^{16}}\\) is equivalent to

1. \\(8a^4\\)
2. \\(8a^8\\)
3. \\(4a^5sqrt3{a}\\)
4. \\(4asqrt3{a^5}\\)

Explanation:

Step1: Split radical into product

$$\sqrt[3]{64a^{16}} = \sqrt[3]{64} \times \sqrt[3]{a^{16}}$$

Step2: Simplify constant radical

$$\sqrt[3]{64} = 4$$

Step3: Split exponent of variable

$$\sqrt[3]{a^{16}} = \sqrt[3]{a^{15} \times a} = \sqrt[3]{a^{15}} \times \sqrt[3]{a} = a^{5}\sqrt[3]{a}$$

Step4: Combine simplified terms

$$4 \times a^{5}\sqrt[3]{a} = 4a^5\sqrt[3]{a}$$

Answer:

1. $4a^5\sqrt[3]{a}$