Basic Math Examples

${(\frac{9 p^{4}}{4 y^{2}})}^{\frac{1}{2}}$

Step 1

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

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Step 1.1

Apply the product rule to $\frac{9 p^{4}}{4 y^{2}}$ .

$\frac{{(9 p^{4})}^{\frac{1}{2}}}{{(4 y^{2})}^{\frac{1}{2}}}$

Step 1.2

Apply the product rule to $9 p^{4}$ .

$\frac{9^{\frac{1}{2}} {(p^{4})}^{\frac{1}{2}}}{{(4 y^{2})}^{\frac{1}{2}}}$

Step 1.3

Apply the product rule to $4 y^{2}$ .

$\frac{9^{\frac{1}{2}} {(p^{4})}^{\frac{1}{2}}}{4^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $9$ as $3^{2}$ .

$\frac{{(3^{2})}^{\frac{1}{2}} {(p^{4})}^{\frac{1}{2}}}{4^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}$

Step 2.2

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

$\frac{3^{2 (\frac{1}{2})} {(p^{4})}^{\frac{1}{2}}}{4^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

$\frac{3^{2 (\frac{1}{2})} {(p^{4})}^{\frac{1}{2}}}{4^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}$

Step 2.3.2

Rewrite the expression.

$\frac{3^{1} {(p^{4})}^{\frac{1}{2}}}{4^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}$

Step 2.4

Evaluate the exponent.

$\frac{3 {(p^{4})}^{\frac{1}{2}}}{4^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}$

Step 2.5

Multiply the exponents in ${(p^{4})}^{\frac{1}{2}}$ .

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Step 2.5.1

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

$\frac{3 p^{4 (\frac{1}{2})}}{4^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}$

Step 2.5.2

Cancel the common factor of $2$ .

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Step 2.5.2.1

Factor $2$ out of $4$ .

$\frac{3 p^{2 (2) \frac{1}{2}}}{4^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}$

Step 2.5.2.2

Cancel the common factor.

$\frac{3 p^{2 \cdot 2 \frac{1}{2}}}{4^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}$

Step 2.5.2.3

Rewrite the expression.

$\frac{3 p^{2}}{4^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{3 p^{2}}{{(2^{2})}^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}$

Step 3.2

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

$\frac{3 p^{2}}{2^{2 (\frac{1}{2})} {(y^{2})}^{\frac{1}{2}}}$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

$\frac{3 p^{2}}{2^{2 (\frac{1}{2})} {(y^{2})}^{\frac{1}{2}}}$

Step 3.3.2

Rewrite the expression.

$\frac{3 p^{2}}{2^{1} {(y^{2})}^{\frac{1}{2}}}$

Step 3.4

Evaluate the exponent.

$\frac{3 p^{2}}{2 {(y^{2})}^{\frac{1}{2}}}$

Step 3.5

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

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Step 3.5.1

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

$\frac{3 p^{2}}{2 y^{2 (\frac{1}{2})}}$

Step 3.5.2

Cancel the common factor of $2$ .

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Step 3.5.2.1

Cancel the common factor.

$\frac{3 p^{2}}{2 y^{2 (\frac{1}{2})}}$

Step 3.5.2.2

Rewrite the expression.

$\frac{3 p^{2}}{2 y^{1}}$

Step 3.6

Simplify.

$\frac{3 p^{2}}{2 y}$