Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Cancel the common factor.

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

Step 1.4

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

Tap for more steps...

Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Add $1$ and $2$ .

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

Step 4.5

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

Tap for more steps...

Step 4.5.1

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

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

Step 4.5.2

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

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

Step 4.5.3

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

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

Step 4.5.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.5.4.1

Cancel the common factor.

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

Step 4.5.4.2

Rewrite the expression.

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

Step 4.5.5

Simplify.

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

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

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

Tap for more steps...

Step 5.4.1

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

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

Step 5.4.2

Multiply $2$ by $2$ .

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

Step 5.5

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

Tap for more steps...

Step 5.5.1

Factor $343$ out of $2401$ .

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

Step 5.5.2

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

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

Step 5.5.3

Factor out $x^{3}$ .

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

Step 5.5.4

Move $7$ .

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

Step 5.5.5

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

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

Step 5.5.6

Add parentheses.

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

Step 5.6

Pull terms out from under the radical.

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

Step 5.7

Combine exponents.

Tap for more steps...

Step 5.7.1

Combine using the product rule for radicals.

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

Step 5.7.2

Multiply $5$ by $7$ .

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

Step 6

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

Tap for more steps...

Step 6.1

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

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

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

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

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

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

Tap for more steps...

Step 7.1

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

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

Step 7.2

Cancel the common factors.

Tap for more steps...

Step 7.2.1

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

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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