Answer:
[tex]2^{\frac{4}{5}}[/tex]
Step-by-step explanation:
Factor 16 using prime factorisation:
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
⇒ 16 = 2⁴
Substitute 16 for 2⁴:
[tex]\implies (\sqrt[5]{16})^1=(\sqrt[5]{2^4})^1[/tex]
[tex]\textsf{Apply exponent rule}\quad \sqrt[n]{a^b} =a^{\frac{b}{n}}:[/tex]
[tex]\implies (\sqrt[5]{2^4})^1=(2^{\frac{4}{5}})^1[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies (2^{\frac{4}{5}})^1=2^{\frac{4}{5}}[/tex]
