Question

Solve (5√16)^1 using prime factorisation.​

Answer 1

Answer:

$2^{\frac{4}{5}}$

Step-by-step explanation:

Factor 16 using prime factorisation:

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

⇒ 16 = 2⁴

Substitute 16  for  2⁴:

$\implies (\sqrt[5]{16})^1=(\sqrt[5]{2^4})^1$

$\textsf{Apply exponent rule}\quad \sqrt[n]{a^b} =a^{\frac{b}{n}}:$

$\implies (\sqrt[5]{2^4})^1=(2^{\frac{4}{5}})^1$

$\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:$

$\implies (2^{\frac{4}{5}})^1=2^{\frac{4}{5}}$