Question

State True or False
The value of $(27\times 125{)}^{\frac{1}{3}}$ is 15.

Answer 1

True
$(27\times 125{)}^{\frac{1}{3}}=(3^3\times 5^3{)}^{\frac{1}{3}}=(3^3{)}^{\frac{1}{3}}\times (5^3{)}^{\frac{1}{3}}(\because a^m\times b^m=(ab{)}^m)=(3{)}^{3\times \frac{1}{3}}\times \left(5{)}^{3\times \frac{1}{3}}\right(\because (a^m{)}^n=a^{mn})$
$=3\times 5=15$
The value of $(27\times 125{)}^{\frac{1}{3}}$ is $15$.