Simplify cube root of (5x^3)/(49x^5)

$\sqrt[3]{\frac{5 x^{3}}{49 x^{5}}}$

Reduce the expression $\frac{5 x^{3}}{49 x^{5}}$ by cancelling the common factors.

Factor $x^{3}$ out of $5 x^{3}$ .

$\sqrt[3]{\frac{x^{3} \cdot 5}{49 x^{5}}}$

Factor $x^{3}$ out of $49 x^{5}$ .

$\sqrt[3]{\frac{x^{3} \cdot 5}{x^{3} (49 x^{2})}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{3} \cdot 5}{x^{3} (49 x^{2})}}$

Rewrite the expression.

$\sqrt[3]{\frac{5}{49 x^{2}}}$

Rewrite $\sqrt[3]{\frac{5}{49 x^{2}}}$ as $\frac{\sqrt[3]{5}}{\sqrt[3]{49 x^{2}}}$ .

$\frac{\sqrt[3]{5}}{\sqrt[3]{49 x^{2}}}$

Multiply $\frac{\sqrt[3]{5}}{\sqrt[3]{49 x^{2}}}$ by $\frac{{\sqrt[3]{49 x^{2}}}^{2}}{{\sqrt[3]{49 x^{2}}}^{2}}$ .

$\frac{\sqrt[3]{5}}{\sqrt[3]{49 x^{2}}} \cdot \frac{{\sqrt[3]{49 x^{2}}}^{2}}{{\sqrt[3]{49 x^{2}}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt[3]{5}}{\sqrt[3]{49 x^{2}}}$ by $\frac{{\sqrt[3]{49 x^{2}}}^{2}}{{\sqrt[3]{49 x^{2}}}^{2}}$ .

$\frac{\sqrt[3]{5} {\sqrt[3]{49 x^{2}}}^{2}}{\sqrt[3]{49 x^{2}} {\sqrt[3]{49 x^{2}}}^{2}}$

Raise $\sqrt[3]{49 x^{2}}$ to the power of $1$ .

$\frac{\sqrt[3]{5} {\sqrt[3]{49 x^{2}}}^{2}}{{\sqrt[3]{49 x^{2}}}^{1} {\sqrt[3]{49 x^{2}}}^{2}}$

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

$\frac{\sqrt[3]{5} {\sqrt[3]{49 x^{2}}}^{2}}{{\sqrt[3]{49 x^{2}}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{\sqrt[3]{5} {\sqrt[3]{49 x^{2}}}^{2}}{{\sqrt[3]{49 x^{2}}}^{3}}$

Rewrite ${\sqrt[3]{49 x^{2}}}^{3}$ as $49 x^{2}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{49 x^{2}}$ as ${(49 x^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{5} {\sqrt[3]{49 x^{2}}}^{2}}{{({(49 x^{2})}^{\frac{1}{3}})}^{3}}$

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

$\frac{\sqrt[3]{5} {\sqrt[3]{49 x^{2}}}^{2}}{{(49 x^{2})}^{\frac{1}{3} \cdot 3}}$

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

$\frac{\sqrt[3]{5} {\sqrt[3]{49 x^{2}}}^{2}}{{(49 x^{2})}^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\sqrt[3]{5} {\sqrt[3]{49 x^{2}}}^{2}}{{(49 x^{2})}^{\frac{3}{3}}}$

Rewrite the expression.

$\frac{\sqrt[3]{5} {\sqrt[3]{49 x^{2}}}^{2}}{{(49 x^{2})}^{1}}$

Simplify.

$\frac{\sqrt[3]{5} {\sqrt[3]{49 x^{2}}}^{2}}{49 x^{2}}$

Simplify the numerator.

Rewrite ${\sqrt[3]{49 x^{2}}}^{2}$ as ${({(49 x^{2})}^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{5} \sqrt[3]{{(49 x^{2})}^{2}}}{49 x^{2}}$

Apply the product rule to $49 x^{2}$ .

$\frac{\sqrt[3]{5} \sqrt[3]{49^{2} {(x^{2})}^{2}}}{49 x^{2}}$

Raise $49$ to the power of $2$ .

$\frac{\sqrt[3]{5} \sqrt[3]{2401 {(x^{2})}^{2}}}{49 x^{2}}$

Multiply the exponents in ${(x^{2})}^{2}$ .

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

$\frac{\sqrt[3]{5} \sqrt[3]{2401 x^{2 \cdot 2}}}{49 x^{2}}$

Multiply $2$ by $2$ .

$\frac{\sqrt[3]{5} \sqrt[3]{2401 x^{4}}}{49 x^{2}}$

Rewrite $2401 x^{4}$ as ${(7 x)}^{3} \cdot (7 x)$ .

Factor $343$ out of $2401$ .

$\frac{\sqrt[3]{5} \sqrt[3]{343 (7) x^{4}}}{49 x^{2}}$

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

$\frac{\sqrt[3]{5} \sqrt[3]{7^{3} \cdot 7 x^{4}}}{49 x^{2}}$

Factor out $x^{3}$ .

$\frac{\sqrt[3]{5} \sqrt[3]{7^{3} \cdot 7 (x^{3} x)}}{49 x^{2}}$

Move $7$ .

$\frac{\sqrt[3]{5} \sqrt[3]{7^{3} x^{3} \cdot 7 x}}{49 x^{2}}$

Rewrite $7^{3} x^{3}$ as ${(7 x)}^{3}$ .

$\frac{\sqrt[3]{5} \sqrt[3]{{(7 x)}^{3} \cdot 7 x}}{49 x^{2}}$

Add parentheses.

$\frac{\sqrt[3]{5} \sqrt[3]{{(7 x)}^{3} \cdot (7 x)}}{49 x^{2}}$

Pull terms out from under the radical.

$\frac{\sqrt[3]{5} \cdot 7 x \sqrt[3]{7 x}}{49 x^{2}}$

Combine exponents.

Combine using the product rule for radicals.

$\frac{7 x \sqrt[3]{5 (7 x)}}{49 x^{2}}$

Multiply $5$ by $7$ .

$\frac{7 x \sqrt[3]{35 x}}{49 x^{2}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $7$ and $49$ .

Factor $7$ out of $7 x \sqrt[3]{35 x}$ .

$\frac{7 (x \sqrt[3]{35 x})}{49 x^{2}}$

Cancel the common factors.

Factor $7$ out of $49 x^{2}$ .

$\frac{7 (x \sqrt[3]{35 x})}{7 (7 x^{2})}$

Cancel the common factor.

$\frac{7 (x \sqrt[3]{35 x})}{7 (7 x^{2})}$

Rewrite the expression.

$\frac{x \sqrt[3]{35 x}}{7 x^{2}}$

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $x \sqrt[3]{35 x}$ .

$\frac{x (\sqrt[3]{35 x})}{7 x^{2}}$

Cancel the common factors.

Factor $x$ out of $7 x^{2}$ .

$\frac{x (\sqrt[3]{35 x})}{x (7 x)}$

Cancel the common factor.

$\frac{x \sqrt[3]{35 x}}{x (7 x)}$

Rewrite the expression.

$\frac{\sqrt[3]{35 x}}{7 x}$

Simplify cube root of (5x^3)/(49x^5)

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