Algebra Examples

$a^{- 4} \cdot {(a^{4} b^{3})}^{2}$

Step 1

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

$\frac{1}{a^{4}} \cdot {(a^{4} b^{3})}^{2}$

Step 2

Apply basic rules of exponents.

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Step 2.1

Apply the product rule to $a^{4} b^{3}$ .

$\frac{1}{a^{4}} \cdot ({(a^{4})}^{2} {(b^{3})}^{2})$

Step 2.2

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

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Step 2.2.1

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

$\frac{1}{a^{4}} \cdot (a^{4 \cdot 2} {(b^{3})}^{2})$

Step 2.2.2

Multiply $4$ by $2$ .

$\frac{1}{a^{4}} \cdot (a^{8} {(b^{3})}^{2})$

Step 3

Cancel the common factor of $a^{4}$ .

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Step 3.1

Factor $a^{4}$ out of $a^{8} {(b^{3})}^{2}$ .

$\frac{1}{a^{4}} \cdot (a^{4} (a^{4} {(b^{3})}^{2}))$

Step 3.2

Cancel the common factor.

$\frac{1}{a^{4}} \cdot (a^{4} (a^{4} {(b^{3})}^{2}))$

Step 3.3

Rewrite the expression.

$a^{4} {(b^{3})}^{2}$

Step 4

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

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Step 4.1

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

$a^{4} b^{3 \cdot 2}$

Step 4.2

Multiply $3$ by $2$ .

$a^{4} b^{6}$