Solve for X (X-1)^(3/2)=27

${(X - 1)}^{\frac{3}{2}} = 27$

Raise each side of the equation to the power of $\frac{2}{3}$ to eliminate the fractional exponent on the left side.

${({(X - 1)}^{\frac{3}{2}})}^{\frac{2}{3}} = 27^{\frac{2}{3}}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(X - 1)}^{\frac{3}{2}})}^{\frac{2}{3}}$ .

Multiply the exponents in ${({(X - 1)}^{\frac{3}{2}})}^{\frac{2}{3}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(X - 1)}^{\frac{3}{2} \cdot \frac{2}{3}} = 27^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(X - 1)}^{\frac{3}{2} \cdot \frac{2}{3}} = 27^{\frac{2}{3}}$

Rewrite the expression.

${(X - 1)}^{\frac{1}{2} \cdot 2} = 27^{\frac{2}{3}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(X - 1)}^{\frac{1}{2} \cdot 2} = 27^{\frac{2}{3}}$

Rewrite the expression.

${(X - 1)}^{1} = 27^{\frac{2}{3}}$

Simplify.

$X - 1 = 27^{\frac{2}{3}}$

Simplify the right side.

Simplify $27^{\frac{2}{3}}$ .

Simplify the expression.

Rewrite $27$ as $3^{3}$ .

$X - 1 = {(3^{3})}^{\frac{2}{3}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$X - 1 = 3^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$X - 1 = 3^{3 (\frac{2}{3})}$

Rewrite the expression.

$X - 1 = 3^{2}$

Raise $3$ to the power of $2$ .

$X - 1 = 9$

Move all terms not containing $X$ to the right side of the equation.

Add $1$ to both sides of the equation.

$X = 9 + 1$

Add $9$ and $1$ .

$X = 10$