Answer to Question #169188 in Algebra for william

Question

Solve (3x-1)^1/3=3

Answer 1

Given:

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

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

$((3x-1)^{\red{\frac{1}{3}}})^\red{3}=27$

Use the following basic rule for exponentiation:

$(a^{b})^c=a^{b \cdot c}$

$(3x-1)^\red{3 \cdot\frac{1}{3}}=27$

$(3x-1)^1=3x-1=27$

$3x-1=27$

$3x-1+\blue1=27+\blue1$

$3x=28$

$x=\frac{28}{3}$

The solution of the given equation:

$x=\frac{28}{3}$