Question 244598
Exponent rules:
{{{(x^a)^b}}} = {{{x^(ab)}}}
.
So, for your problem:
{{{t^(2/3)= 4}}}
I could raise both to the reciprocal power (3/2) to both sides:
{{{(t^(2/3))^(3/2)= 4^(3/2)}}}
{{{t^(2/3 *3/2)= 4^(3/2)}}}
{{{t^1= 4^(3/2)}}}
{{{t = 4^(3/2)}}}
We can rewrite the right side as:
{{{t = (4^3)^(1/2)}}}
But, raising something to the 1/2 is essentially taking the square root:
{{{t = sqrt(4^3)}}}
{{{t = sqrt(4*4*4)}}}
We can take "pairs" out from under the radical:
{{{t = 4sqrt(4)}}}
{{{t = 4*2}}}
{{{t = 8}}}