Pre-Algebra Examples

$\frac{3 ({(- 2)}^{4} k^{20})}{{(k^{3})}^{- 4}}$

Step 1

Move ${(k^{3})}^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3 ({(- 2)}^{4} k^{20}) {(k^{3})}^{4}$

Step 2

Raise $- 2$ to the power of $4$ .

$3 (16 k^{20}) {(k^{3})}^{4}$

Step 3

Multiply $16$ by $3$ .

$48 k^{20} {(k^{3})}^{4}$

Step 4

Multiply the exponents in ${(k^{3})}^{4}$ .

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Step 4.1

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

$48 k^{20} k^{3 \cdot 4}$

Step 4.2

Multiply $3$ by $4$ .

$48 k^{20} k^{12}$

Step 5

Multiply $k^{20}$ by $k^{12}$ by adding the exponents.

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Step 5.1

Move $k^{12}$ .

$48 (k^{12} k^{20})$

Step 5.2

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

$48 k^{12 + 20}$

Step 5.3

Add $12$ and $20$ .

$48 k^{32}$