Basic Math Examples

${(5 y^{5} z^{- 4})}^{2}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Multiply $5 y^{5} \frac{1}{z^{4}}$ .

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Step 2.1

Combine $5$ and $\frac{1}{z^{4}}$ .

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

Step 2.2

Combine $y^{5}$ and $\frac{5}{z^{4}}$ .

${(\frac{y^{5} \cdot 5}{z^{4}})}^{2}$

Step 3

Move $5$ to the left of $y^{5}$ .

${(\frac{5 \cdot y^{5}}{z^{4}})}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $\frac{5 y^{5}}{z^{4}}$ .

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

Step 4.2

Apply the product rule to $5 y^{5}$ .

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

Step 5

Simplify the numerator.

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Step 5.1

Raise $5$ to the power of $2$ .

$\frac{25 {(y^{5})}^{2}}{{(z^{4})}^{2}}$

Step 5.2

Multiply the exponents in ${(y^{5})}^{2}$ .

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Step 5.2.1

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

$\frac{25 y^{5 \cdot 2}}{{(z^{4})}^{2}}$

Step 5.2.2

Multiply $5$ by $2$ .

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

Step 6

Multiply the exponents in ${(z^{4})}^{2}$ .

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Step 6.1

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

$\frac{25 y^{10}}{z^{4 \cdot 2}}$

Step 6.2

Multiply $4$ by $2$ .

$\frac{25 y^{10}}{z^{8}}$