I Need Help With This Math Question.

I need help with this math question.

Answer:

x = -54/5

Step-by-step explanation:

$\bigg(\dfrac{1}{64} \bigg)^{\frac{x}{2} + 1 }=\bigg(\dfrac{1}{16} \bigg)^{\frac{x}{3} -3 }$

Change both fractions to have a base number of 2:

$\bigg(\dfrac{1}{2^6} \bigg)^{\frac{x}{2} + 1 } = \bigg(\dfrac{1}{2^4} \bigg)^{\frac{x}{3} -3 }$

$\bigg(\dfrac{1}{2} \bigg)^{6(\frac{x}{2} + 1) } = \bigg(\dfrac{1}{2} \bigg)^{4(\frac{x}{3} -3) }$

Since both numbers are 1/2, the exponent must be equal:

$6(\dfrac{x}{2} + 1) = 4(\dfrac{x}{3} -3)$

$3x + 6 = \dfrac{4x}{3} -12$

$3x - \dfrac{4x}{3} = -12 - 6$

$\dfrac{5x}{3} = -18$

$5x = -54$

$x = -54/5$

Answer: x = -54/5

Brushcoverm