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Answer:
x = 3.
Step-by-step explanation:
Given:
[tex](8x-8)^{\frac{3}{2} } = 64[/tex]
Rule of fractions in exponents:
Numerator- power
Denominator- root
Take the 2/3 root of both sides:
[tex](8x-8) = 64x^{\frac{2}{3} }[/tex]
Simplify [tex]64x^{\frac{2}{3} }[/tex]
Cube root of 64 = 4
4² = 16.
Therefore:
8x - 8 = 16
Add 8 to both sides:
8x = 24
Divide both sides by 8:
x = 3.
