Basic Math Examples

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

Step 1

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

${(8 y^{3})}^{2} y^{3}$

Step 2

Apply the product rule to $8 y^{3}$ .

$8^{2} {(y^{3})}^{2} y^{3}$

Step 3

Raise $8$ to the power of $2$ .

$64 {(y^{3})}^{2} y^{3}$

Step 4

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

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Step 4.1

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

$64 y^{3 \cdot 2} y^{3}$

Step 4.2

Multiply $3$ by $2$ .

$64 y^{6} y^{3}$

Step 5

Multiply $y^{6}$ by $y^{3}$ by adding the exponents.

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Step 5.1

Move $y^{3}$ .

$64 (y^{3} y^{6})$

Step 5.2

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

$64 y^{3 + 6}$

Step 5.3

Add $3$ and $6$ .

$64 y^{9}$