Basic Math Examples

${(64 a^{2} y^{3})}^{\frac{1}{2}}$

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 $64 a^{2} y^{3}$ .

${(64 a^{2})}^{\frac{1}{2}} {(y^{3})}^{\frac{1}{2}}$

Step 1.2

Apply the product rule to $64 a^{2}$ .

$64^{\frac{1}{2}} {(a^{2})}^{\frac{1}{2}} {(y^{3})}^{\frac{1}{2}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $64$ as $8^{2}$ .

${(8^{2})}^{\frac{1}{2}} {(a^{2})}^{\frac{1}{2}} {(y^{3})}^{\frac{1}{2}}$

Step 2.2

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

$8^{2 (\frac{1}{2})} {(a^{2})}^{\frac{1}{2}} {(y^{3})}^{\frac{1}{2}}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$8^{2 (\frac{1}{2})} {(a^{2})}^{\frac{1}{2}} {(y^{3})}^{\frac{1}{2}}$

Step 3.2

Rewrite the expression.

$8^{1} {(a^{2})}^{\frac{1}{2}} {(y^{3})}^{\frac{1}{2}}$

Step 4

Simplify the expression.

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Step 4.1

Evaluate the exponent.

$8 {(a^{2})}^{\frac{1}{2}} {(y^{3})}^{\frac{1}{2}}$

Step 4.2

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

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Step 4.2.1

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

$8 a^{2 (\frac{1}{2})} {(y^{3})}^{\frac{1}{2}}$

Step 4.2.2

Cancel the common factor of $2$ .

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Step 4.2.2.1

Cancel the common factor.

$8 a^{2 (\frac{1}{2})} {(y^{3})}^{\frac{1}{2}}$

Step 4.2.2.2

Rewrite the expression.

$8 a^{1} {(y^{3})}^{\frac{1}{2}}$

Step 5

Simplify.

$8 a {(y^{3})}^{\frac{1}{2}}$

Step 6

Multiply the exponents in ${(y^{3})}^{\frac{1}{2}}$ .

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Step 6.1

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

$8 a y^{3 (\frac{1}{2})}$

Step 6.2

Combine $3$ and $\frac{1}{2}$ .

$8 a y^{\frac{3}{2}}$