Algebra Examples

$5 x^{4} y^{2} \sqrt{\frac{4}{25}} x^{20} y^{30}$

Step 1

Multiply $x^{4}$ by $x^{20}$ by adding the exponents.

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Step 1.1

Move $x^{20}$ .

$5 (x^{20} x^{4}) y^{2} \sqrt{\frac{4}{25}} y^{30}$

Step 1.2

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

$5 x^{20 + 4} y^{2} \sqrt{\frac{4}{25}} y^{30}$

Step 1.3

Add $20$ and $4$ .

$5 x^{24} y^{2} \sqrt{\frac{4}{25}} y^{30}$

Step 2

Multiply $y^{2}$ by $y^{30}$ by adding the exponents.

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Step 2.1

Move $y^{30}$ .

$5 x^{24} (y^{30} y^{2}) \sqrt{\frac{4}{25}}$

Step 2.2

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

$5 x^{24} y^{30 + 2} \sqrt{\frac{4}{25}}$

Step 2.3

Add $30$ and $2$ .

$5 x^{24} y^{32} \sqrt{\frac{4}{25}}$

Step 3

Rewrite $\sqrt{\frac{4}{25}}$ as $\frac{\sqrt{4}}{\sqrt{25}}$ .

$5 x^{24} y^{32} \frac{\sqrt{4}}{\sqrt{25}}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite $4$ as $2^{2}$ .

$5 x^{24} y^{32} \frac{\sqrt{2^{2}}}{\sqrt{25}}$

Step 4.2

Pull terms out from under the radical, assuming positive real numbers.

$5 x^{24} y^{32} \frac{2}{\sqrt{25}}$

Step 5

Simplify the denominator.

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Step 5.1

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

$5 x^{24} y^{32} \frac{2}{\sqrt{5^{2}}}$

Step 5.2

Pull terms out from under the radical, assuming positive real numbers.

$5 x^{24} y^{32} \frac{2}{5}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Cancel the common factor of $5$ .

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Step 6.1.1

Factor $5$ out of $5 x^{24} y^{32}$ .

$5 (x^{24} y^{32}) \frac{2}{5}$

Step 6.1.2

Cancel the common factor.

$5 (x^{24} y^{32}) \frac{2}{5}$

Step 6.1.3

Rewrite the expression.

$x^{24} y^{32} \cdot 2$

Step 6.2

Move $2$ to the left of $x^{24} y^{32}$ .

$2 x^{24} y^{32}$