Checkpoint: Exponential Equations Solution

Solve.

$216 = {(\frac{1}{6})}^{3 - x}$

$216 = 6^{3} \frac{1}{6} = 6^{- 1} 6^{3} = 6^{- 1 (3 - x)} 3 = - 1 (3 - x) 3 = - 3 + x x = 6$

Note

Q: Why are negative exponents useful when solving equations?
A: If a base is in the denominator you can use a negative exponent to take its reciprocal.