Basic Math Examples

${(c^{- 2})}^{\frac{2}{3}} c^{\frac{3}{2}} \div c^{- 3}$

Step 1

Rewrite the division as a fraction.

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

Step 2

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

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

Step 3

Multiply $c^{\frac{3}{2}}$ by $c^{3}$ by adding the exponents.

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Step 3.1

Move $c^{3}$ .

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

Step 3.2

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

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

Step 3.3

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

${(c^{- 2})}^{\frac{2}{3}} c^{3 \cdot \frac{2}{2} + \frac{3}{2}}$

Step 3.4

Combine $3$ and $\frac{2}{2}$ .

${(c^{- 2})}^{\frac{2}{3}} c^{\frac{3 \cdot 2}{2} + \frac{3}{2}}$

Step 3.5

Combine the numerators over the common denominator.

${(c^{- 2})}^{\frac{2}{3}} c^{\frac{3 \cdot 2 + 3}{2}}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $3$ by $2$ .

${(c^{- 2})}^{\frac{2}{3}} c^{\frac{6 + 3}{2}}$

Step 3.6.2

Add $6$ and $3$ .

${(c^{- 2})}^{\frac{2}{3}} c^{\frac{9}{2}}$

Step 4

Multiply the exponents in ${(c^{- 2})}^{\frac{2}{3}}$ .

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Step 4.1

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

$c^{- 2 (\frac{2}{3})} c^{\frac{9}{2}}$

Step 4.2

Multiply $- 2 (\frac{2}{3})$ .

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Step 4.2.1

Combine $- 2$ and $\frac{2}{3}$ .

$c^{\frac{- 2 \cdot 2}{3}} c^{\frac{9}{2}}$

Step 4.2.2

Multiply $- 2$ by $2$ .

$c^{\frac{- 4}{3}} c^{\frac{9}{2}}$

Step 4.3

Move the negative in front of the fraction.

$c^{- \frac{4}{3}} c^{\frac{9}{2}}$

Step 5

Multiply $c^{- \frac{4}{3}}$ by $c^{\frac{9}{2}}$ by adding the exponents.

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Step 5.1

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

$c^{- \frac{4}{3} + \frac{9}{2}}$

Step 5.2

To write $- \frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$c^{- \frac{4}{3} \cdot \frac{2}{2} + \frac{9}{2}}$

Step 5.3

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$c^{- \frac{4}{3} \cdot \frac{2}{2} + \frac{9}{2} \cdot \frac{3}{3}}$

Step 5.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.4.1

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$c^{- \frac{4 \cdot 2}{3 \cdot 2} + \frac{9}{2} \cdot \frac{3}{3}}$

Step 5.4.2

Multiply $3$ by $2$ .

$c^{- \frac{4 \cdot 2}{6} + \frac{9}{2} \cdot \frac{3}{3}}$

Step 5.4.3

Multiply $\frac{9}{2}$ by $\frac{3}{3}$ .

$c^{- \frac{4 \cdot 2}{6} + \frac{9 \cdot 3}{2 \cdot 3}}$

Step 5.4.4

Multiply $2$ by $3$ .

$c^{- \frac{4 \cdot 2}{6} + \frac{9 \cdot 3}{6}}$

Step 5.5

Combine the numerators over the common denominator.

$c^{\frac{- 4 \cdot 2 + 9 \cdot 3}{6}}$

Step 5.6

Simplify the numerator.

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Step 5.6.1

Multiply $- 4$ by $2$ .

$c^{\frac{- 8 + 9 \cdot 3}{6}}$

Step 5.6.2

Multiply $9$ by $3$ .

$c^{\frac{- 8 + 27}{6}}$

Step 5.6.3

Add $- 8$ and $27$ .

$c^{\frac{19}{6}}$