Basic Math Examples

$\sqrt{25 a^{5}} \cdot \sqrt{25 a^{5}}$

Step 1

Rewrite $25 a^{5}$ as ${(5 a^{2})}^{2} a$ .

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Step 1.1

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} a^{5}} \cdot \sqrt{25 a^{5}}$

Step 1.2

Factor out $a^{4}$ .

$\sqrt{5^{2} (a^{4} a)} \cdot \sqrt{25 a^{5}}$

Step 1.3

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$\sqrt{5^{2} ({(a^{2})}^{2} a)} \cdot \sqrt{25 a^{5}}$

Step 1.4

Rewrite $5^{2} {(a^{2})}^{2}$ as ${(5 a^{2})}^{2}$ .

$\sqrt{{(5 a^{2})}^{2} a} \cdot \sqrt{25 a^{5}}$

Step 2

Pull terms out from under the radical.

$5 a^{2} \sqrt{a} \cdot \sqrt{25 a^{5}}$

Step 3

Rewrite $25 a^{5}$ as ${(5 a^{2})}^{2} a$ .

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Step 3.1

Rewrite $25$ as $5^{2}$ .

$5 a^{2} \sqrt{a} \cdot \sqrt{5^{2} a^{5}}$

Step 3.2

Factor out $a^{4}$ .

$5 a^{2} \sqrt{a} \cdot \sqrt{5^{2} (a^{4} a)}$

Step 3.3

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$5 a^{2} \sqrt{a} \cdot \sqrt{5^{2} ({(a^{2})}^{2} a)}$

Step 3.4

Rewrite $5^{2} {(a^{2})}^{2}$ as ${(5 a^{2})}^{2}$ .

$5 a^{2} \sqrt{a} \cdot \sqrt{{(5 a^{2})}^{2} a}$

Step 4

Pull terms out from under the radical.

$5 a^{2} \sqrt{a} \cdot (5 a^{2} \sqrt{a})$

Step 5

Multiply $a^{2}$ by $a^{2}$ by adding the exponents.

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Step 5.1

Move $a^{2}$ .

$5 (a^{2} a^{2}) \sqrt{a} \cdot (5 \sqrt{a})$

Step 5.2

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

$5 a^{2 + 2} \sqrt{a} \cdot (5 \sqrt{a})$

Step 5.3

Add $2$ and $2$ .

$5 a^{4} \sqrt{a} \cdot (5 \sqrt{a})$

Step 6

Multiply $5 a^{4} \sqrt{a} (5 \sqrt{a})$ .

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Step 6.1

Multiply $5$ by $5$ .

$25 a^{4} \sqrt{a} \sqrt{a}$

Step 6.2

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

$25 a^{4} ({\sqrt{a}}^{1} \sqrt{a})$

Step 6.3

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

$25 a^{4} ({\sqrt{a}}^{1} {\sqrt{a}}^{1})$

Step 6.4

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

$25 a^{4} {\sqrt{a}}^{1 + 1}$

Step 6.5

Add $1$ and $1$ .

$25 a^{4} {\sqrt{a}}^{2}$

Step 7

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

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Step 7.1

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

$25 a^{4} {(a^{\frac{1}{2}})}^{2}$

Step 7.2

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

$25 a^{4} a^{\frac{1}{2} \cdot 2}$

Step 7.3

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

$25 a^{4} a^{\frac{2}{2}}$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$25 a^{4} a^{\frac{2}{2}}$

Step 7.4.2

Rewrite the expression.

$25 a^{4} a^{1}$

Step 7.5

Simplify.

$25 a^{4} a$

Step 8

Multiply $a^{4}$ by $a$ by adding the exponents.

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Step 8.1

Move $a$ .

$25 (a \cdot a^{4})$

Step 8.2

Multiply $a$ by $a^{4}$ .

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Step 8.2.1

Raise $a$ to the power of $1$ .

$25 (a^{1} a^{4})$

Step 8.2.2

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

$25 a^{1 + 4}$

Step 8.3

Add $1$ and $4$ .

$25 a^{5}$