Basic Math Examples

$\frac{5 c^{- 3} p^{3}}{{(y^{- 2})}^{- 3}} \cdot \frac{y^{3} p^{3}}{{(c^{3})}^{- 4}}$

Step 1

Combine.

$\frac{5 c^{- 3} p^{3} (y^{3} p^{3})}{{(y^{- 2})}^{- 3} {(c^{3})}^{- 4}}$

Step 2

Multiply $p^{3}$ by $p^{3}$ by adding the exponents.

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Step 2.1

Move $p^{3}$ .

$\frac{5 c^{- 3} (p^{3} p^{3}) y^{3}}{{(y^{- 2})}^{- 3} {(c^{3})}^{- 4}}$

Step 2.2

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

$\frac{5 c^{- 3} p^{3 + 3} y^{3}}{{(y^{- 2})}^{- 3} {(c^{3})}^{- 4}}$

Step 2.3

Add $3$ and $3$ .

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

Step 3

Simplify.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Move ${(c^{3})}^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 4

Simplify the numerator.

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

Multiply $- 2$ by $3$ .

$\frac{5 p^{6} y^{3} y^{- 6} {(c^{3})}^{4}}{c^{3}}$

Step 4.2

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

$\frac{5 p^{6} y^{3} \frac{1}{y^{6}} {(c^{3})}^{4}}{c^{3}}$

Step 4.3

Multiply the exponents in ${(c^{3})}^{4}$ .

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Step 4.3.1

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

$\frac{5 p^{6} y^{3} \frac{1}{y^{6}} c^{3 \cdot 4}}{c^{3}}$

Step 4.3.2

Multiply $3$ by $4$ .

$\frac{5 p^{6} y^{3} \frac{1}{y^{6}} c^{12}}{c^{3}}$

Step 4.4

Combine exponents.

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Step 4.4.1

Combine $5$ and $\frac{1}{y^{6}}$ .

$\frac{p^{6} y^{3} \frac{5}{y^{6}} c^{12}}{c^{3}}$

Step 4.4.2

Combine $p^{6}$ and $\frac{5}{y^{6}}$ .

$\frac{y^{3} \frac{p^{6} \cdot 5}{y^{6}} c^{12}}{c^{3}}$

Step 4.4.3

Combine $y^{3}$ and $\frac{p^{6} \cdot 5}{y^{6}}$ .

$\frac{\frac{y^{3} (p^{6} \cdot 5)}{y^{6}} c^{12}}{c^{3}}$

Step 4.4.4

Combine $\frac{y^{3} (p^{6} \cdot 5)}{y^{6}}$ and $c^{12}$ .

$\frac{\frac{y^{3} (p^{6} \cdot 5) c^{12}}{y^{6}}}{c^{3}}$

Step 4.5

Remove unnecessary parentheses.

$\frac{\frac{y^{3} p^{6} \cdot 5 c^{12}}{y^{6}}}{c^{3}}$

Step 4.6

Reduce the expression $\frac{y^{3} p^{6} \cdot 5 c^{12}}{y^{6}}$ by cancelling the common factors.

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Step 4.6.1

Factor $y^{3}$ out of $y^{3} p^{6} \cdot 5 c^{12}$ .

$\frac{\frac{y^{3} (p^{6} \cdot 5 c^{12})}{y^{6}}}{c^{3}}$

Step 4.6.2

Factor $y^{3}$ out of $y^{6}$ .

$\frac{\frac{y^{3} (p^{6} \cdot 5 c^{12})}{y^{3} y^{3}}}{c^{3}}$

Step 4.6.3

Cancel the common factor.

$\frac{\frac{y^{3} (p^{6} \cdot 5 c^{12})}{y^{3} y^{3}}}{c^{3}}$

Step 4.6.4

Rewrite the expression.

$\frac{\frac{p^{6} \cdot 5 c^{12}}{y^{3}}}{c^{3}}$

Step 4.7

Move $5$ to the left of $p^{6}$ .

$\frac{\frac{5 p^{6} c^{12}}{y^{3}}}{c^{3}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 p^{6} c^{12}}{y^{3}} \cdot \frac{1}{c^{3}}$

Step 6

Combine.

$\frac{5 p^{6} c^{12} \cdot 1}{y^{3} c^{3}}$

Step 7

Cancel the common factor of $c^{12}$ and $c^{3}$ .

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Step 7.1

Factor $c^{3}$ out of $5 p^{6} c^{12} \cdot 1$ .

$\frac{c^{3} (5 p^{6} c^{9} \cdot 1)}{y^{3} c^{3}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $c^{3}$ out of $y^{3} c^{3}$ .

$\frac{c^{3} (5 p^{6} c^{9} \cdot 1)}{c^{3} y^{3}}$

Step 7.2.2

Cancel the common factor.

$\frac{c^{3} (5 p^{6} c^{9} \cdot 1)}{c^{3} y^{3}}$

Step 7.2.3

Rewrite the expression.

$\frac{5 p^{6} c^{9} \cdot 1}{y^{3}}$

Step 8

Multiply $5$ by $1$ .

$\frac{5 p^{6} c^{9}}{y^{3}}$