Basic Math Examples

{(5 \sqrt{15})}^{2}

${(5 \sqrt{15})}^{2}$

Step 1

Simplify the expression.

Tap for more steps...

Step 1.1

Apply the product rule to

5 \sqrt{15}

$5 \sqrt{15}$ .

5^{2} {\sqrt{15}}^{2}

$5^{2} {\sqrt{15}}^{2}$

Step 1.2

Raise

5

$5$ to the power of

2

$2$ .

25 {\sqrt{15}}^{2}

$25 {\sqrt{15}}^{2}$

25 {\sqrt{15}}^{2}

$25 {\sqrt{15}}^{2}$

Step 2

Rewrite

{\sqrt{15}}^{2}

${\sqrt{15}}^{2}$ as

15

$15$ .

Tap for more steps...

Step 2.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{15}

$\sqrt{15}$ as

15^{\frac{1}{2}}

$15^{\frac{1}{2}}$ .

25 {(15^{\frac{1}{2}})}^{2}

$25 {(15^{\frac{1}{2}})}^{2}$

Step 2.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

25 \cdot 15^{\frac{1}{2} \cdot 2}

$25 \cdot 15^{\frac{1}{2} \cdot 2}$

Step 2.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

25 \cdot 15^{\frac{2}{2}}

$25 \cdot 15^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of

2

$2$ .

Tap for more steps...

Step 2.4.1

Cancel the common factor.

$25 \cdot 15^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

$25 \cdot 15^{1}$

$25 \cdot 15^{1}$

Step 2.5

Evaluate the exponent.

$25 \cdot 15$

$25 \cdot 15$

Step 3

Multiply

$25$ by

$15$ .

$375$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$