Algebra Examples

$\sqrt{{(7 x)}^{3}}$

Step 1

Apply the product rule to $7 x$ .

$\sqrt{7^{3} x^{3}}$

Step 2

Raise $7$ to the power of $3$ .

$\sqrt{343 x^{3}}$

Step 3

Rewrite $\sqrt{343 x^{3}}$ as $\sqrt{343} \sqrt{x^{3}}$ .

$\sqrt{343} \sqrt{x^{3}}$

Step 4

Multiply to rationalize the numerator.

$\frac{\sqrt{x^{3}} (\sqrt{343} \sqrt{343})}{\sqrt{343}}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Raise $\sqrt{343}$ to the power of $1$ .

$\frac{\sqrt{x^{3}} ({\sqrt{343}}^{1} \sqrt{343})}{\sqrt{343}}$

Step 5.2

Raise $\sqrt{343}$ to the power of $1$ .

$\frac{\sqrt{x^{3}} ({\sqrt{343}}^{1} {\sqrt{343}}^{1})}{\sqrt{343}}$

Step 5.3

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

$\frac{\sqrt{x^{3}} {\sqrt{343}}^{1 + 1}}{\sqrt{343}}$

Step 5.4

Add $1$ and $1$ .

$\frac{\sqrt{x^{3}} {\sqrt{343}}^{2}}{\sqrt{343}}$

Step 5.5

Rewrite ${\sqrt{343}}^{2}$ as $343$ .

Tap for more steps...

Step 5.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{343}$ as $343^{\frac{1}{2}}$ .

$\frac{\sqrt{x^{3}} {(343^{\frac{1}{2}})}^{2}}{\sqrt{343}}$

Step 5.5.2

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

$\frac{\sqrt{x^{3}} \cdot 343^{\frac{1}{2} \cdot 2}}{\sqrt{343}}$

Step 5.5.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{\sqrt{x^{3}} \cdot 343^{\frac{2}{2}}}{\sqrt{343}}$

Step 5.5.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.5.4.1

Cancel the common factor.

$\frac{\sqrt{x^{3}} \cdot 343^{\frac{2}{2}}}{\sqrt{343}}$

Step 5.5.4.2

Rewrite the expression.

$\frac{\sqrt{x^{3}} \cdot 343^{1}}{\sqrt{343}}$

Step 5.5.5

Evaluate the exponent.

$\frac{\sqrt{x^{3}} \cdot 343}{\sqrt{343}}$

Step 6

Multiply to rationalize the numerator.

$\frac{343 (\sqrt{x^{3}} \sqrt{x^{3}})}{\sqrt{343} \sqrt{x^{3}}}$

Step 7

Simplify.

Tap for more steps...

Step 7.1

Raise $\sqrt{x^{3}}$ to the power of $1$ .

$\frac{343 ({\sqrt{x^{3}}}^{1} \sqrt{x^{3}})}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.2

Raise $\sqrt{x^{3}}$ to the power of $1$ .

$\frac{343 ({\sqrt{x^{3}}}^{1} {\sqrt{x^{3}}}^{1})}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.3

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

$\frac{343 {\sqrt{x^{3}}}^{1 + 1}}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.4

Add $1$ and $1$ .

$\frac{343 {\sqrt{x^{3}}}^{2}}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.5

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

Tap for more steps...

Step 7.5.1

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

$\frac{343 {(x^{\frac{3}{2}})}^{2}}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.5.2

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

$\frac{343 x^{\frac{3}{2} \cdot 2}}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.5.3

Combine $\frac{3}{2}$ and $2$ .

$\frac{343 x^{\frac{3 \cdot 2}{2}}}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.5.4

Multiply $3$ by $2$ .

$\frac{343 x^{\frac{6}{2}}}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.5.5

Cancel the common factor of $6$ and $2$ .

Tap for more steps...

Step 7.5.5.1

Factor $2$ out of $6$ .

$\frac{343 x^{\frac{2 \cdot 3}{2}}}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.5.5.2

Cancel the common factors.

Tap for more steps...

Step 7.5.5.2.1

Factor $2$ out of $2$ .

$\frac{343 x^{\frac{2 \cdot 3}{2 (1)}}}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.5.5.2.2

Cancel the common factor.

$\frac{343 x^{\frac{2 \cdot 3}{2 \cdot 1}}}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.5.5.2.3

Rewrite the expression.

$\frac{343 x^{\frac{3}{1}}}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.5.5.2.4

Divide $3$ by $1$ .

$\frac{343 x^{3}}{\sqrt{343} \sqrt{x^{3}}}$

Step 7.6

Rewrite $343$ as $7^{2} \cdot 7$ .

Tap for more steps...

Step 7.6.1

Factor $49$ out of $343$ .

$\frac{343 x^{3}}{\sqrt{49 (7)} \sqrt{x^{3}}}$

Step 7.6.2

Rewrite $49$ as $7^{2}$ .

$\frac{343 x^{3}}{\sqrt{7^{2} \cdot 7} \sqrt{x^{3}}}$

Step 7.7

Pull terms out from under the radical.

$\frac{343 x^{3}}{7 \sqrt{7} \sqrt{x^{3}}}$

Step 7.8

Factor out $x^{2}$ .

$\frac{343 x^{3}}{7 \sqrt{7} \sqrt{x^{2} x}}$

Step 7.9

Pull terms out from under the radical.

$\frac{343 x^{3}}{7 \sqrt{7} (x \sqrt{x})}$

Step 7.10

Combine using the product rule for radicals.

$\frac{343 x^{3}}{7 x \sqrt{7 x}}$