Answer: 8
Step-by-step explanation:
Recall from the law of indices ;
Given [tex]a^{\frac{m}{n}}[/tex] , it could be written as [tex]\sqrt[n]{a^{m}}[/tex]
Therefore :
[tex]16^{\frac{3}{4}}[/tex] can be written as :
[tex]\sqrt[4]{16}) ^{3}[/tex]
The fourth root of 16 = 2 that is 2x2x2x2 = 16
so the expression [tex]\sqrt[4]{16}) ^{3}[/tex] becomes
[tex]2^{3}[/tex]
which will be 8
Therefore :
[tex]16^{\frac{3}{4}}[/tex] = 8
