Solve for x 1/7(x+9)^(3/2)=49

$\frac{1}{7} {(x + 9)}^{\frac{3}{2}} = 49$

Multiply both sides of the equation by $7$ .

$7 (\frac{1}{7} \cdot {(x + 9)}^{\frac{3}{2}}) = 7 \cdot 49$

Simplify both sides of the equation.

Simplify the left side.

Simplify $7 (\frac{1}{7} \cdot {(x + 9)}^{\frac{3}{2}})$ .

Combine $\frac{1}{7}$ and ${(x + 9)}^{\frac{3}{2}}$ .

$7 \frac{{(x + 9)}^{\frac{3}{2}}}{7} = 7 \cdot 49$

Cancel the common factor of $7$ .

Cancel the common factor.

$7 \frac{{(x + 9)}^{\frac{3}{2}}}{7} = 7 \cdot 49$

Rewrite the expression.

${(x + 9)}^{\frac{3}{2}} = 7 \cdot 49$

Simplify the right side.

Multiply $7$ by $49$ .

${(x + 9)}^{\frac{3}{2}} = 343$

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

${({(x + 9)}^{\frac{3}{2}})}^{\frac{2}{3}} = 343^{\frac{2}{3}}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(x + 9)}^{\frac{3}{2}})}^{\frac{2}{3}}$ .

Multiply the exponents in ${({(x + 9)}^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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

${(x + 9)}^{\frac{3}{2} \cdot \frac{2}{3}} = 343^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(x + 9)}^{\frac{3}{2} \cdot \frac{2}{3}} = 343^{\frac{2}{3}}$

Rewrite the expression.

${(x + 9)}^{\frac{1}{2} \cdot 2} = 343^{\frac{2}{3}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 9)}^{\frac{1}{2} \cdot 2} = 343^{\frac{2}{3}}$

Rewrite the expression.

${(x + 9)}^{1} = 343^{\frac{2}{3}}$

Simplify.

$x + 9 = 343^{\frac{2}{3}}$

Simplify the right side.

Simplify $343^{\frac{2}{3}}$ .

Simplify the expression.

Rewrite $343$ as $7^{3}$ .

$x + 9 = {(7^{3})}^{\frac{2}{3}}$

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

$x + 9 = 7^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x + 9 = 7^{3 (\frac{2}{3})}$

Rewrite the expression.

$x + 9 = 7^{2}$

Raise $7$ to the power of $2$ .

$x + 9 = 49$

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

Subtract $9$ from both sides of the equation.

$x = 49 - 9$

Subtract $9$ from $49$ .

$x = 40$

Solve for x 1/7(x+9)^(3/2)=49

Related Questions

Support LCMGCF.com by disabling your adblocker.