Question

Which of the following is equivalent to (16^3/2)^1/2? 6 8 12 64

Answer 1

Answer:

Option B is correct that is 8.

Step-by-step explanation:

Given Expression : $(16^{\frac{3}{2}})^{\frac{1}{2}}$

We use a law of exponent here to simplify it,

$(x^a)^b=x^{ab}$

Consider,

$(16^{\frac{3}{2}})^{\frac{1}{2}}$

$=16^{\frac{3}{2}\times\frac{1}{2}}$

$=16^{\frac{3}{4}}$

$=(2^4)^{\frac{3}{4}}$

$=2^{4\times\frac{3}{4}}$

$=2^3$

$=8$

Therefore, Option B is correct that is 8.

Answer 2

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ \left( 16^{\frac{3}{2}} \right)^{\frac{1}{2}}\implies 16^{\frac{3}{2}\cdot \frac{1}{2}}\implies 16^{\frac{3}{4}}\qquad \boxed{16=2^4}\qquad (2^4)^{\frac{3}{4}}\implies 2^{4\cdot \frac{3}{4}} \\\\\\ 2^3\implies 8$