Algebra Examples

$\frac{3^{2} m^{4} t^{8}}{3^{4} m^{9} t^{- 4}}$

Step 1

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

$\frac{3^{2} m^{4} t^{8} t^{4}}{3^{4} m^{9}}$

Step 2

Multiply $t^{8}$ by $t^{4}$ by adding the exponents.

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Step 2.1

Move $t^{4}$ .

$\frac{3^{2} m^{4} (t^{4} t^{8})}{3^{4} m^{9}}$

Step 2.2

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

$\frac{3^{2} m^{4} t^{4 + 8}}{3^{4} m^{9}}$

Step 2.3

Add $4$ and $8$ .

$\frac{3^{2} m^{4} t^{12}}{3^{4} m^{9}}$

Step 3

Cancel the common factor of $3^{2}$ and $3^{4}$ .

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Step 3.1

Factor $3^{2}$ out of $3^{2} m^{4} t^{12}$ .

$\frac{3^{2} (m^{4} t^{12})}{3^{4} m^{9}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3^{2}$ out of $3^{4} m^{9}$ .

$\frac{3^{2} (m^{4} t^{12})}{3^{2} (3^{2} m^{9})}$

Step 3.2.2

Cancel the common factor.

$\frac{3^{2} (m^{4} t^{12})}{3^{2} (3^{2} m^{9})}$

Step 3.2.3

Rewrite the expression.

$\frac{m^{4} t^{12}}{3^{2} m^{9}}$

Step 4

Cancel the common factor of $m^{4}$ and $m^{9}$ .

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Step 4.1

Factor $m^{4}$ out of $m^{4} t^{12}$ .

$\frac{m^{4} (t^{12})}{3^{2} m^{9}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $m^{4}$ out of $3^{2} m^{9}$ .

$\frac{m^{4} (t^{12})}{m^{4} (3^{2} m^{5})}$

Step 4.2.2

Cancel the common factor.

$\frac{m^{4} t^{12}}{m^{4} (3^{2} m^{5})}$

Step 4.2.3

Rewrite the expression.

$\frac{t^{12}}{3^{2} m^{5}}$

Step 5

Raise $3$ to the power of $2$ .

$\frac{t^{12}}{9 m^{5}}$