Basic Math Examples

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

Step 1

Multiply $b^{- 2}$ by $b$ by adding the exponents.

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Step 1.1

Move $b$ .

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

Step 1.2

Multiply $b$ by $b^{- 2}$ .

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Step 1.2.1

Raise $b$ to the power of $1$ .

${(\frac{2 a^{0} (b^{1} b^{- 2}) c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}$

Step 1.2.2

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

${(\frac{2 a^{0} b^{1 - 2} c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}$

Step 1.3

Subtract $2$ from $1$ .

${(\frac{2 a^{0} b^{- 1} c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}$

Step 2

Simplify $2 a^{0} b^{- 1} c^{- 3}$ .

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

Step 3

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

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

Step 4

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

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

Step 5

Multiply $c^{4}$ by $c^{3}$ by adding the exponents.

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Step 5.1

Move $c^{3}$ .

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

Step 5.2

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

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

Step 5.3

Add $3$ and $4$ .

${(\frac{2}{2 a^{- 3} c^{7} b})}^{- 3}$

Step 6

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

${(\frac{2 a^{3}}{2 c^{7} b})}^{- 3}$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Cancel the common factor.

${(\frac{2 a^{3}}{2 c^{7} b})}^{- 3}$

Step 7.2

Rewrite the expression.

${(\frac{a^{3}}{c^{7} b})}^{- 3}$

Step 8

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{c^{7} b}{a^{3}})}^{3}$

Step 9

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 9.1

Apply the product rule to $\frac{c^{7} b}{a^{3}}$ .

$\frac{{(c^{7} b)}^{3}}{{(a^{3})}^{3}}$

Step 9.2

Apply the product rule to $c^{7} b$ .

$\frac{{(c^{7})}^{3} b^{3}}{{(a^{3})}^{3}}$

Step 10

Multiply the exponents in ${(c^{7})}^{3}$ .

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Step 10.1

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

$\frac{c^{7 \cdot 3} b^{3}}{{(a^{3})}^{3}}$

Step 10.2

Multiply $7$ by $3$ .

$\frac{c^{21} b^{3}}{{(a^{3})}^{3}}$

Step 11

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

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Step 11.1

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

$\frac{c^{21} b^{3}}{a^{3 \cdot 3}}$

Step 11.2

Multiply $3$ by $3$ .

$\frac{c^{21} b^{3}}{a^{9}}$