Question

Determine the solution for the following equation: %3D64" id="TexFormula1" title="(8x-8)^{\frac{3}{2} }=64" alt="(8x-8)^{\frac{3}{2} }=64" align="absmiddle" class="latex-formula">
a - x=3
b - x=5
c - 13
d - 65

Answer 1

Answer:

$\text{A. }x=3$

Step-by-step explanation:

Recall the exponent property $a^{b^c}=a^{(b\cdot c)}$. Therefore, we can square both sides of the equation to get rid of the fraction in the exponent:

$((8x-8)^{\frac{3}{2}})^2=64^2,\\(8x-8)^{\frac{3}{2}\cdot2}=64^2,\\(8x-8)^3=4096$

Take the cube root of both sides:

$8x-8=16$

Add 8 to both sides:

$8x=24$

Divide both sides by 8 to isolate $x$:

$x=\frac{24}{8}=\boxed{3}$