Basic Math Examples

${(\frac{2 a^{0} b^{4}}{a^{- 2} b^{2}})}^{3}$

Step 1

Move $a^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{2 a^{0} b^{4} a^{2}}{b^{2}})}^{3}$

Step 2

Multiply $a^{0}$ by $a^{2}$ by adding the exponents.

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Step 2.1

Move $a^{2}$ .

${(\frac{2 (a^{2} a^{0}) b^{4}}{b^{2}})}^{3}$

Step 2.2

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

${(\frac{2 a^{2 + 0} b^{4}}{b^{2}})}^{3}$

Step 2.3

Add $2$ and $0$ .

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

Step 3

Cancel the common factor of $b^{4}$ and $b^{2}$ .

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Step 3.1

Factor $b^{2}$ out of $2 a^{2} b^{4}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $2 a^{2} b^{2}$ by $1$ .

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

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 $2 a^{2} b^{2}$ .

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

Step 4.2

Apply the product rule to $2 a^{2}$ .

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

Step 5

Raise $2$ to the power of $3$ .

$8 {(a^{2})}^{3} {(b^{2})}^{3}$

Step 6

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

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Step 6.1

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

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

Step 6.2

Multiply $2$ by $3$ .

$8 a^{6} {(b^{2})}^{3}$

Step 7

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

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Step 7.1

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

$8 a^{6} b^{2 \cdot 3}$

Step 7.2

Multiply $2$ by $3$ .

$8 a^{6} b^{6}$