Rewrite the following expression using the properties of rational exponents. Be sure your answer is in simplest form. (2•6)3/2

Question

asked Dec 10, 2020 137k views

1 Answer

Fjodr · Answer 1 · 2020-12-13T23:21:53+0000

Answer:

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

Explanation:

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

We multiply within the parenthesis to get:

$(12)^{(3)/(2)}$

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

We apply this property to get:

$(12)^{(3)/(2)}=√(12^3)$

$(12)^{(3)/(2)}=√(12^2*12)$

This simplifies to

$(12)^{(3)/(2)}=12√(12)$

We can simplify further

$(12)^{(3)/(2)}=12√(4*3)=12*2√(3)=24√(3)$

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