Evaluate Using the Given Value 1 , 125=9x^3

$1$ , $125 = 9 x^{3}$

Rewrite the equation as $9 x^{3} = 125$ .

$9 x^{3} = 125$

Divide each term in $9 x^{3} = 125$ by $9$ and simplify.

Divide each term in $9 x^{3} = 125$ by $9$ .

$\frac{9 x^{3}}{9} = \frac{125}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{3}}{9} = \frac{125}{9}$

Divide $x^{3}$ by $1$ .

$x^{3} = \frac{125}{9}$

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{\frac{125}{9}}$

Simplify $\sqrt[3]{\frac{125}{9}}$ .

Rewrite $\sqrt[3]{\frac{125}{9}}$ as $\frac{\sqrt[3]{125}}{\sqrt[3]{9}}$ .

$x = \frac{\sqrt[3]{125}}{\sqrt[3]{9}}$

Simplify the numerator.

Rewrite $125$ as $5^{3}$ .

$x = \frac{\sqrt[3]{5^{3}}}{\sqrt[3]{9}}$

Pull terms out from under the radical, assuming real numbers.

$x = \frac{5}{\sqrt[3]{9}}$

Multiply $\frac{5}{\sqrt[3]{9}}$ by $\frac{{\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{2}}$ .

$x = \frac{5}{\sqrt[3]{9}} \cdot \frac{{\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{5}{\sqrt[3]{9}}$ by $\frac{{\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{2}}$ .

$x = \frac{5 {\sqrt[3]{9}}^{2}}{\sqrt[3]{9} {\sqrt[3]{9}}^{2}}$

Raise $\sqrt[3]{9}$ to the power of $1$ .

$x = \frac{5 {\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{1} {\sqrt[3]{9}}^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \frac{5 {\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{1 + 2}}$

Add $1$ and $2$ .

$x = \frac{5 {\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{3}}$

Rewrite ${\sqrt[3]{9}}^{3}$ as $9$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{9}$ as $9^{\frac{1}{3}}$ .

$x = \frac{5 {\sqrt[3]{9}}^{2}}{{(9^{\frac{1}{3}})}^{3}}$

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

$x = \frac{5 {\sqrt[3]{9}}^{2}}{9^{\frac{1}{3} \cdot 3}}$

Combine $\frac{1}{3}$ and $3$ .

$x = \frac{5 {\sqrt[3]{9}}^{2}}{9^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x = \frac{5 {\sqrt[3]{9}}^{2}}{9^{\frac{3}{3}}}$

Rewrite the expression.

$x = \frac{5 {\sqrt[3]{9}}^{2}}{9^{1}}$

Evaluate the exponent.

$x = \frac{5 {\sqrt[3]{9}}^{2}}{9}$

Simplify the numerator.

Rewrite ${\sqrt[3]{9}}^{2}$ as ${(9^{2})}^{\frac{1}{3}}$ .

$x = \frac{5 \sqrt[3]{9^{2}}}{9}$

Raise $9$ to the power of $2$ .

$x = \frac{5 \sqrt[3]{81}}{9}$

Rewrite $81$ as $3^{3} \cdot 3$ .

Factor $27$ out of $81$ .

$x = \frac{5 \sqrt[3]{27 (3)}}{9}$

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

$x = \frac{5 \sqrt[3]{3^{3} \cdot 3}}{9}$

Pull terms out from under the radical.

$x = \frac{5 \cdot 3 \sqrt[3]{3}}{9}$

Multiply $5$ by $3$ .

$x = \frac{15 \sqrt[3]{3}}{9}$

Cancel the common factor of $15$ and $9$ .

Factor $3$ out of $15 \sqrt[3]{3}$ .

$x = \frac{3 (5 \sqrt[3]{3})}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$x = \frac{3 (5 \sqrt[3]{3})}{3 (3)}$

Cancel the common factor.

$x = \frac{3 (5 \sqrt[3]{3})}{3 \cdot 3}$

Rewrite the expression.

$x = \frac{5 \sqrt[3]{3}}{3}$

Replace the variable $x$ with $\frac{5 \sqrt[3]{3}}{3}$ in the expression.

$1$

Evaluate Using the Given Value 1 , 125=9x^3

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