Question

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

Answer 1

`2^{(4)/(5)}`

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^{(b)/(n)}:`

`\implies (\sqrt[5]{2^4})^1=(2^{(4)/(5)})^1`

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

`\implies (2^{(4)/(5)})^1=2^{(4)/(5)}`