Algebra Examples

$\frac{r^{- 3} s^{5} t^{2}}{r^{2} s t^{- 2}}$

Step 1

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

$\frac{s^{5} t^{2}}{r^{2} s t^{- 2} r^{3}}$

Step 2

Multiply $r^{2}$ by $r^{3}$ by adding the exponents.

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Step 2.1

Move $r^{3}$ .

$\frac{s^{5} t^{2}}{r^{3} r^{2} s t^{- 2}}$

Step 2.2

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

$\frac{s^{5} t^{2}}{r^{3 + 2} s t^{- 2}}$

Step 2.3

Add $3$ and $2$ .

$\frac{s^{5} t^{2}}{r^{5} s t^{- 2}}$

Step 3

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

$\frac{s^{5} t^{2} t^{2}}{r^{5} s}$

Step 4

Multiply $t^{2}$ by $t^{2}$ by adding the exponents.

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Step 4.1

Move $t^{2}$ .

$\frac{s^{5} (t^{2} t^{2})}{r^{5} s}$

Step 4.2

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

$\frac{s^{5} t^{2 + 2}}{r^{5} s}$

Step 4.3

Add $2$ and $2$ .

$\frac{s^{5} t^{4}}{r^{5} s}$

Step 5

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

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Step 5.1

Factor $s$ out of $s^{5} t^{4}$ .

$\frac{s (s^{4} t^{4})}{r^{5} s}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $s$ out of $r^{5} s$ .

$\frac{s (s^{4} t^{4})}{s r^{5}}$

Step 5.2.2

Cancel the common factor.

$\frac{s (s^{4} t^{4})}{s r^{5}}$

Step 5.2.3

Rewrite the expression.

$\frac{s^{4} t^{4}}{r^{5}}$