Algebra Examples

$\frac{- 12 t^{- 1} u^{5} x^{- 4}}{2 t^{- 3} u x^{5}}$

Step 1

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

$\frac{- 12 t^{- 1} u^{5}}{2 t^{- 3} u x^{5} x^{4}}$

Step 2

Multiply $x^{5}$ by $x^{4}$ by adding the exponents.

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Step 2.1

Move $x^{4}$ .

$\frac{- 12 t^{- 1} u^{5}}{2 t^{- 3} u (x^{4} x^{5})}$

Step 2.2

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

$\frac{- 12 t^{- 1} u^{5}}{2 t^{- 3} u x^{4 + 5}}$

Step 2.3

Add $4$ and $5$ .

$\frac{- 12 t^{- 1} u^{5}}{2 t^{- 3} u x^{9}}$

Step 3

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

$\frac{- 12 t^{- 1} u^{5} t^{3}}{2 u x^{9}}$

Step 4

Multiply $t^{- 1}$ by $t^{3}$ by adding the exponents.

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Step 4.1

Move $t^{3}$ .

$\frac{- 12 (t^{3} t^{- 1}) u^{5}}{2 u x^{9}}$

Step 4.2

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

$\frac{- 12 t^{3 - 1} u^{5}}{2 u x^{9}}$

Step 4.3

Subtract $1$ from $3$ .

$\frac{- 12 t^{2} u^{5}}{2 u x^{9}}$

Step 5

Cancel the common factor of $- 12$ and $2$ .

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Step 5.1

Factor $2$ out of $- 12 t^{2} u^{5}$ .

$\frac{2 (- 6 t^{2} u^{5})}{2 u x^{9}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $2 u x^{9}$ .

$\frac{2 (- 6 t^{2} u^{5})}{2 (u x^{9})}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (- 6 t^{2} u^{5})}{2 (u x^{9})}$

Step 5.2.3

Rewrite the expression.

$\frac{- 6 t^{2} u^{5}}{u x^{9}}$

Step 6

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

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Step 6.1

Factor $u$ out of $- 6 t^{2} u^{5}$ .

$\frac{u (- 6 t^{2} u^{4})}{u x^{9}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $u$ out of $u x^{9}$ .

$\frac{u (- 6 t^{2} u^{4})}{u (x^{9})}$

Step 6.2.2

Cancel the common factor.

$\frac{u (- 6 t^{2} u^{4})}{u x^{9}}$

Step 6.2.3

Rewrite the expression.

$\frac{- 6 t^{2} u^{4}}{x^{9}}$

Step 7

Move the negative in front of the fraction.

$- \frac{6 t^{2} u^{4}}{x^{9}}$