Question

Determine the solution for the following equation:
`(8x-8)^{(3)/(2) }=64`

a - x=3
b - x=5
c - 13
d - 65

Answer 1

`\text{A. }x=3`

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)^{(3)/(2)})^2=64^2,\\(8x-8)^{(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=(24)/(8)=\boxed{3}`