Basic Math Examples

${(\frac{6 c^{\frac{5}{2}} s^{5}}{c^{4} s^{- \frac{3}{2}}})}^{- 2}$

Step 1

Move $c^{\frac{5}{2}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

${(\frac{6 s^{5}}{c^{4} s^{- \frac{3}{2}} c^{- \frac{5}{2}}})}^{- 2}$

Step 2

Multiply $c^{4}$ by $c^{- \frac{5}{2}}$ by adding the exponents.

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Step 2.1

Move $c^{- \frac{5}{2}}$ .

${(\frac{6 s^{5}}{c^{- \frac{5}{2}} c^{4} s^{- \frac{3}{2}}})}^{- 2}$

Step 2.2

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

${(\frac{6 s^{5}}{c^{- \frac{5}{2} + 4} s^{- \frac{3}{2}}})}^{- 2}$

Step 2.3

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

${(\frac{6 s^{5}}{c^{- \frac{5}{2} + 4 \cdot \frac{2}{2}} s^{- \frac{3}{2}}})}^{- 2}$

Step 2.4

Combine $4$ and $\frac{2}{2}$ .

${(\frac{6 s^{5}}{c^{- \frac{5}{2} + \frac{4 \cdot 2}{2}} s^{- \frac{3}{2}}})}^{- 2}$

Step 2.5

Combine the numerators over the common denominator.

${(\frac{6 s^{5}}{c^{\frac{- 5 + 4 \cdot 2}{2}} s^{- \frac{3}{2}}})}^{- 2}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $4$ by $2$ .

${(\frac{6 s^{5}}{c^{\frac{- 5 + 8}{2}} s^{- \frac{3}{2}}})}^{- 2}$

Step 2.6.2

Add $- 5$ and $8$ .

${(\frac{6 s^{5}}{c^{\frac{3}{2}} s^{- \frac{3}{2}}})}^{- 2}$

Step 3

Move $s^{- \frac{3}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{6 s^{5} s^{\frac{3}{2}}}{c^{\frac{3}{2}}})}^{- 2}$

Step 4

Multiply $s^{5}$ by $s^{\frac{3}{2}}$ by adding the exponents.

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Step 4.1

Move $s^{\frac{3}{2}}$ .

${(\frac{6 (s^{\frac{3}{2}} s^{5})}{c^{\frac{3}{2}}})}^{- 2}$

Step 4.2

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

${(\frac{6 s^{\frac{3}{2} + 5}}{c^{\frac{3}{2}}})}^{- 2}$

Step 4.3

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

${(\frac{6 s^{\frac{3}{2} + 5 \cdot \frac{2}{2}}}{c^{\frac{3}{2}}})}^{- 2}$

Step 4.4

Combine $5$ and $\frac{2}{2}$ .

${(\frac{6 s^{\frac{3}{2} + \frac{5 \cdot 2}{2}}}{c^{\frac{3}{2}}})}^{- 2}$

Step 4.5

Combine the numerators over the common denominator.

${(\frac{6 s^{\frac{3 + 5 \cdot 2}{2}}}{c^{\frac{3}{2}}})}^{- 2}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $5$ by $2$ .

${(\frac{6 s^{\frac{3 + 10}{2}}}{c^{\frac{3}{2}}})}^{- 2}$

Step 4.6.2

Add $3$ and $10$ .

${(\frac{6 s^{\frac{13}{2}}}{c^{\frac{3}{2}}})}^{- 2}$

Step 5

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

${(\frac{c^{\frac{3}{2}}}{6 s^{\frac{13}{2}}})}^{2}$

Step 6

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

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Step 6.1

Apply the product rule to $\frac{c^{\frac{3}{2}}}{6 s^{\frac{13}{2}}}$ .

$\frac{{(c^{\frac{3}{2}})}^{2}}{{(6 s^{\frac{13}{2}})}^{2}}$

Step 6.2

Apply the product rule to $6 s^{\frac{13}{2}}$ .

$\frac{{(c^{\frac{3}{2}})}^{2}}{6^{2} {(s^{\frac{13}{2}})}^{2}}$

Step 7

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

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Step 7.1

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

$\frac{c^{\frac{3}{2} \cdot 2}}{6^{2} {(s^{\frac{13}{2}})}^{2}}$

Step 7.2

Cancel the common factor of $2$ .

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Step 7.2.1

Cancel the common factor.

$\frac{c^{\frac{3}{2} \cdot 2}}{6^{2} {(s^{\frac{13}{2}})}^{2}}$

Step 7.2.2

Rewrite the expression.

$\frac{c^{3}}{6^{2} {(s^{\frac{13}{2}})}^{2}}$

Step 8

Simplify the denominator.

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Step 8.1

Raise $6$ to the power of $2$ .

$\frac{c^{3}}{36 {(s^{\frac{13}{2}})}^{2}}$

Step 8.2

Multiply the exponents in ${(s^{\frac{13}{2}})}^{2}$ .

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Step 8.2.1

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

$\frac{c^{3}}{36 s^{\frac{13}{2} \cdot 2}}$

Step 8.2.2

Cancel the common factor of $2$ .

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Step 8.2.2.1

Cancel the common factor.

$\frac{c^{3}}{36 s^{\frac{13}{2} \cdot 2}}$

Step 8.2.2.2

Rewrite the expression.

$\frac{c^{3}}{36 s^{13}}$