Finite Math Examples

$\frac{3^{2} m^{5} t^{6}}{3^{5} m^{7} t^{- 5}}$

Step 1

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

$\frac{3^{2} m^{5} t^{6} t^{5}}{3^{5} m^{7}}$

Step 2

Multiply $t^{6}$ by $t^{5}$ by adding the exponents.

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Step 2.1

Move $t^{5}$ .

$\frac{3^{2} m^{5} (t^{5} t^{6})}{3^{5} m^{7}}$

Step 2.2

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

$\frac{3^{2} m^{5} t^{5 + 6}}{3^{5} m^{7}}$

Step 2.3

Add $5$ and $6$ .

$\frac{3^{2} m^{5} t^{11}}{3^{5} m^{7}}$

Step 3

Cancel the common factor of $3^{2}$ and $3^{5}$ .

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Step 3.1

Factor $3^{2}$ out of $3^{2} m^{5} t^{11}$ .

$\frac{3^{2} (m^{5} t^{11})}{3^{5} m^{7}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3^{2}$ out of $3^{5} m^{7}$ .

$\frac{3^{2} (m^{5} t^{11})}{3^{2} (3^{3} m^{7})}$

Step 3.2.2

Cancel the common factor.

$\frac{3^{2} (m^{5} t^{11})}{3^{2} (3^{3} m^{7})}$

Step 3.2.3

Rewrite the expression.

$\frac{m^{5} t^{11}}{3^{3} m^{7}}$

Step 4

Cancel the common factor of $m^{5}$ and $m^{7}$ .

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Step 4.1

Factor $m^{5}$ out of $m^{5} t^{11}$ .

$\frac{m^{5} (t^{11})}{3^{3} m^{7}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $m^{5}$ out of $3^{3} m^{7}$ .

$\frac{m^{5} (t^{11})}{m^{5} (3^{3} m^{2})}$

Step 4.2.2

Cancel the common factor.

$\frac{m^{5} t^{11}}{m^{5} (3^{3} m^{2})}$

Step 4.2.3

Rewrite the expression.

$\frac{t^{11}}{3^{3} m^{2}}$

Step 5

Raise $3$ to the power of $3$ .

$\frac{t^{11}}{27 m^{2}}$