### Home > GB8I > Chapter 8 Unit 9 > Lesson INT1: 8.1.6 > Problem8-84

8-84.

Determine values for a and b that make each system of equations true (i.e., solve each system). Be sure to show your work or explain your thinking clearly.

1. $6 = a \cdot b ^ { 0 }$
$24 = a \cdot b ^ { 2 }$

What is $b^{0}$ equivalent to?

Once you have the value for $a$ use it to solve for $b$ in second equation.

1. $32 = a \cdot b ^ { 2 }$
$128 = a \cdot b ^ { 3 }$

Solve both equations for $a$.

Set both equations equal to each other (Equal Values Method), and multiply both sides by the common denominator of both fractions.

Solve for $b$ and substitute $b$ back into one of the original equations to solve for $a$.

$a = 2$, $b = 4$