Algebra Examples

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

Step 1

Combine $\frac{4}{25}$ and $x^{20}$ .

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

Step 2

Combine $\frac{4 x^{20}}{25}$ and $y^{30}$ .

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

Step 3

Rewrite $4 x^{20} y^{30}$ as ${(2 x^{10} y^{15})}^{2}$ .

$5 x^{4} y^{2} \sqrt{\frac{{(2 x^{10} y^{15})}^{2}}{25}}$

Step 4

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

$5 x^{4} y^{2} \sqrt{\frac{{(2 x^{10} y^{15})}^{2}}{5^{2}}}$

Step 5

Rewrite $\frac{{(2 x^{10} y^{15})}^{2}}{5^{2}}$ as ${(\frac{2 x^{10} y^{15}}{5})}^{2}$ .

$5 x^{4} y^{2} \sqrt{{(\frac{2 x^{10} y^{15}}{5})}^{2}}$

Step 6

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

$5 x^{4} y^{2} \frac{2 x^{10} y^{15}}{5}$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Factor $5$ out of $5 x^{4} y^{2}$ .

$5 (x^{4} y^{2}) \frac{2 x^{10} y^{15}}{5}$

Step 7.2

Cancel the common factor.

$5 (x^{4} y^{2}) \frac{2 x^{10} y^{15}}{5}$

Step 7.3

Rewrite the expression.

$x^{4} y^{2} (2 x^{10} y^{15})$

Step 8

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

$x^{10 + 4} y^{2} (2 y^{15})$

Step 9

Add $10$ and $4$ .

$x^{14} y^{2} (2 y^{15})$

Step 10

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

$x^{14} (2 y^{2 + 15})$

Step 11

Add $2$ and $15$ .

$x^{14} (2 y^{17})$

Step 12

Rewrite using the commutative property of multiplication.

$2 x^{14} y^{17}$