Basic Math Examples

${(9 c^{2} y^{\frac{1}{2}} z^{3})}^{2}$

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 $9 c^{2} y^{\frac{1}{2}} z^{3}$ .

${(9 c^{2} y^{\frac{1}{2}})}^{2} {(z^{3})}^{2}$

Step 1.2

Apply the product rule to $9 c^{2} y^{\frac{1}{2}}$ .

${(9 c^{2})}^{2} {(y^{\frac{1}{2}})}^{2} {(z^{3})}^{2}$

Step 1.3

Apply the product rule to $9 c^{2}$ .

$9^{2} {(c^{2})}^{2} {(y^{\frac{1}{2}})}^{2} {(z^{3})}^{2}$

Step 2

Raise $9$ to the power of $2$ .

$81 {(c^{2})}^{2} {(y^{\frac{1}{2}})}^{2} {(z^{3})}^{2}$

Step 3

Multiply the exponents in ${(c^{2})}^{2}$ .

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Step 3.1

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

$81 c^{2 \cdot 2} {(y^{\frac{1}{2}})}^{2} {(z^{3})}^{2}$

Step 3.2

Multiply $2$ by $2$ .

$81 c^{4} {(y^{\frac{1}{2}})}^{2} {(z^{3})}^{2}$

Step 4

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

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Step 4.1

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

$81 c^{4} y^{\frac{1}{2} \cdot 2} {(z^{3})}^{2}$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Cancel the common factor.

$81 c^{4} y^{\frac{1}{2} \cdot 2} {(z^{3})}^{2}$

Step 4.2.2

Rewrite the expression.

$81 c^{4} y^{1} {(z^{3})}^{2}$

Step 5

Simplify.

$81 c^{4} y {(z^{3})}^{2}$

Step 6

Multiply the exponents in ${(z^{3})}^{2}$ .

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Step 6.1

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

$81 c^{4} y z^{3 \cdot 2}$

Step 6.2

Multiply $3$ by $2$ .

$81 c^{4} y z^{6}$