Pre-Algebra Examples

${(\frac{12 x^{8}}{75 y^{10}})}^{\frac{1}{2}}$

Step 1

Cancel the common factor of $12$ and $75$ .

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Step 1.1

Factor $3$ out of $12 x^{8}$ .

${(\frac{3 (4 x^{8})}{75 y^{10}})}^{\frac{1}{2}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $75 y^{10}$ .

${(\frac{3 (4 x^{8})}{3 (25 y^{10})})}^{\frac{1}{2}}$

Step 1.2.2

Cancel the common factor.

${(\frac{3 (4 x^{8})}{3 (25 y^{10})})}^{\frac{1}{2}}$

Step 1.2.3

Rewrite the expression.

${(\frac{4 x^{8}}{25 y^{10}})}^{\frac{1}{2}}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $\frac{4 x^{8}}{25 y^{10}}$ .

$\frac{{(4 x^{8})}^{\frac{1}{2}}}{{(25 y^{10})}^{\frac{1}{2}}}$

Step 2.2

Apply the product rule to $4 x^{8}$ .

$\frac{4^{\frac{1}{2}} {(x^{8})}^{\frac{1}{2}}}{{(25 y^{10})}^{\frac{1}{2}}}$

Step 2.3

Apply the product rule to $25 y^{10}$ .

$\frac{4^{\frac{1}{2}} {(x^{8})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{{(2^{2})}^{\frac{1}{2}} {(x^{8})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Step 3.2

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

$\frac{2^{2 (\frac{1}{2})} {(x^{8})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

$\frac{2^{2 (\frac{1}{2})} {(x^{8})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Step 3.3.2

Rewrite the expression.

$\frac{2^{1} {(x^{8})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Step 3.4

Evaluate the exponent.

$\frac{2 {(x^{8})}^{\frac{1}{2}}}{25^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Step 3.5

Multiply the exponents in ${(x^{8})}^{\frac{1}{2}}$ .

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Step 3.5.1

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

$\frac{2 x^{8 (\frac{1}{2})}}{25^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Step 3.5.2

Cancel the common factor of $2$ .

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Step 3.5.2.1

Factor $2$ out of $8$ .

$\frac{2 x^{2 (4) \frac{1}{2}}}{25^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Step 3.5.2.2

Cancel the common factor.

$\frac{2 x^{2 \cdot 4 \frac{1}{2}}}{25^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Step 3.5.2.3

Rewrite the expression.

$\frac{2 x^{4}}{25^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Step 4

Simplify the denominator.

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Step 4.1

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

$\frac{2 x^{4}}{{(5^{2})}^{\frac{1}{2}} {(y^{10})}^{\frac{1}{2}}}$

Step 4.2

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

$\frac{2 x^{4}}{5^{2 (\frac{1}{2})} {(y^{10})}^{\frac{1}{2}}}$

Step 4.3

Cancel the common factor of $2$ .

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Step 4.3.1

Cancel the common factor.

$\frac{2 x^{4}}{5^{2 (\frac{1}{2})} {(y^{10})}^{\frac{1}{2}}}$

Step 4.3.2

Rewrite the expression.

$\frac{2 x^{4}}{5^{1} {(y^{10})}^{\frac{1}{2}}}$

Step 4.4

Evaluate the exponent.

$\frac{2 x^{4}}{5 {(y^{10})}^{\frac{1}{2}}}$

Step 4.5

Multiply the exponents in ${(y^{10})}^{\frac{1}{2}}$ .

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Step 4.5.1

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

$\frac{2 x^{4}}{5 y^{10 (\frac{1}{2})}}$

Step 4.5.2

Cancel the common factor of $2$ .

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Step 4.5.2.1

Factor $2$ out of $10$ .

$\frac{2 x^{4}}{5 y^{2 (5) \frac{1}{2}}}$

Step 4.5.2.2

Cancel the common factor.

$\frac{2 x^{4}}{5 y^{2 \cdot 5 \frac{1}{2}}}$

Step 4.5.2.3

Rewrite the expression.

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