Question

Rewrite the following expression using the properties of rational exponents. Be sure your answer is in simplest form.

Answer 1

Answer:

$(2\cdot 6)^{\frac{3}{2}}=24(3)^{\frac{1}{2}}$

Step-by-step explanation:

The given expression is $(2*6)^{\frac{3}{2}}$

We multiply within the parenthesis to get:

$(12)^{\frac{3}{2}}$

Recall that: $a^{\frac{m}{n} } =\sqrt[n]{x^m}$

We apply this property to get:

$(12)^{\frac{3}{2}}=\sqrt{12^3}$

$(12)^{\frac{3}{2}}=\sqrt{12^2*12}$

This simplifies to

$(12)^{\frac{3}{2}}=12\sqrt{12}$

We can simplify further

$(12)^{\frac{3}{2}}=12\sqrt{4*3}=12*2\sqrt{3}=24\sqrt{3}$

We rewrite as rational exponent  $24(3)^{\frac{1}{2}}$