Basic Math Examples

$\frac{{(4 y^{5})}^{4}}{y^{- 3}}$

Step 1

Move $y^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(4 y^{5})}^{4} y^{3}$

Step 2

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

$4^{4} {(y^{5})}^{4} y^{3}$

Step 3

Raise $4$ to the power of $4$ .

$256 {(y^{5})}^{4} y^{3}$

Step 4

Multiply the exponents in ${(y^{5})}^{4}$ .

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Step 4.1

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

$256 y^{5 \cdot 4} y^{3}$

Step 4.2

Multiply $5$ by $4$ .

$256 y^{20} y^{3}$

Step 5

Multiply $y^{20}$ by $y^{3}$ by adding the exponents.

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Step 5.1

Move $y^{3}$ .

$256 (y^{3} y^{20})$

Step 5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$256 y^{3 + 20}$

Step 5.3

Add $3$ and $20$ .

$256 y^{23}$