Finite Math Examples

$\frac{3^{- 1} {(p^{- 2})}^{3}}{3 p^{- 7}}$

Step 1

Simplify the expression.

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Step 1.1

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

$\frac{{(p^{- 2})}^{3}}{3 p^{- 7} \cdot 3}$

Step 1.2

Multiply $3$ by $3$ .

$\frac{{(p^{- 2})}^{3}}{9 p^{- 7}}$

Step 1.3

Move $p^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(p^{- 2})}^{3} p^{7}}{9}$

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

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

$\frac{p^{- 2 \cdot 3} p^{7}}{9}$

Step 2.1.2

Multiply $- 2$ by $3$ .

$\frac{p^{- 6} p^{7}}{9}$

Step 2.2

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

$\frac{\frac{1}{p^{6}} p^{7}}{9}$

Step 3

Combine $\frac{1}{p^{6}}$ and $p^{7}$ .

$\frac{\frac{p^{7}}{p^{6}}}{9}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Reduce the expression $\frac{p^{7}}{p^{6}}$ by cancelling the common factors.

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Step 4.1.1

Factor $p^{6}$ out of $p^{7}$ .

$\frac{\frac{p^{6} p}{p^{6}}}{9}$

Step 4.1.2

Multiply by $1$ .

$\frac{\frac{p^{6} p}{p^{6} \cdot 1}}{9}$

Step 4.1.3

Cancel the common factor.

$\frac{\frac{p^{6} p}{p^{6} \cdot 1}}{9}$

Step 4.1.4

Rewrite the expression.

$\frac{\frac{p}{1}}{9}$

Step 4.2

Divide $p$ by $1$ .

$\frac{p}{9}$