Solve for x 3(x-2)^(3/4)=24

$3 {(x - 2)}^{\frac{3}{4}} = 24$

Step 1

Divide each term in $3 {(x - 2)}^{\frac{3}{4}} = 24$ by $3$ and simplify.

Divide each term in $3 {(x - 2)}^{\frac{3}{4}} = 24$ by $3$ .

$\frac{3 {(x - 2)}^{\frac{3}{4}}}{3} = \frac{24}{3}$

Simplify the left side.

Cancel the common factor.

$\frac{3 {(x - 2)}^{\frac{3}{4}}}{3} = \frac{24}{3}$

Divide ${(x - 2)}^{\frac{3}{4}}$ by $1$ .

${(x - 2)}^{\frac{3}{4}} = \frac{24}{3}$

Simplify the right side.

Divide $24$ by $3$ .

${(x - 2)}^{\frac{3}{4}} = 8$

Step 2

Raise each side of the equation to the power of $\frac{4}{3}$ to eliminate the fractional exponent on the left side.

${({(x - 2)}^{\frac{3}{4}})}^{\frac{4}{3}} = 8^{\frac{4}{3}}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${({(x - 2)}^{\frac{3}{4}})}^{\frac{4}{3}}$ .

Multiply the exponents in ${({(x - 2)}^{\frac{3}{4}})}^{\frac{4}{3}}$ .

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

${(x - 2)}^{\frac{3}{4} \cdot \frac{4}{3}} = 8^{\frac{4}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(x - 2)}^{\frac{3}{4} \cdot \frac{4}{3}} = 8^{\frac{4}{3}}$

Rewrite the expression.

${(x - 2)}^{\frac{1}{4} \cdot 4} = 8^{\frac{4}{3}}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(x - 2)}^{\frac{1}{4} \cdot 4} = 8^{\frac{4}{3}}$

Rewrite the expression.

${(x - 2)}^{1} = 8^{\frac{4}{3}}$

Simplify.

$x - 2 = 8^{\frac{4}{3}}$

Simplify the right side.

Simplify $8^{\frac{4}{3}}$ .

Simplify the expression.

Rewrite $8$ as $2^{3}$ .

$x - 2 = {(2^{3})}^{\frac{4}{3}}$

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

$x - 2 = 2^{3 (\frac{4}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x - 2 = 2^{3 (\frac{4}{3})}$

Rewrite the expression.

$x - 2 = 2^{4}$

Raise $2$ to the power of $4$ .

$x - 2 = 16$

Step 4

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

Add $2$ to both sides of the equation.

$x = 16 + 2$

Add $16$ and $2$ .

$x = 18$

Solve for x 3(x-2)^(3/4)=24

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