Algebra Examples

${(\frac{r^{- 1} s^{2} t^{- 3}}{r^{- 2} s^{0} t^{1}})}^{- 1}$

Step 1

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

${(\frac{r^{- 1} s^{2}}{r^{- 2} s^{0} t \cdot t^{3}})}^{- 1}$

Step 2

Simplify the denominator.

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Step 2.1

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

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Step 2.1.1

Move $t^{3}$ .

${(\frac{r^{- 1} s^{2}}{r^{- 2} s^{0} (t^{3} t)})}^{- 1}$

Step 2.1.2

Multiply $t^{3}$ by $t$ .

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Step 2.1.2.1

Raise $t$ to the power of $1$ .

${(\frac{r^{- 1} s^{2}}{r^{- 2} s^{0} (t^{3} t^{1})})}^{- 1}$

Step 2.1.2.2

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

${(\frac{r^{- 1} s^{2}}{r^{- 2} s^{0} t^{3 + 1}})}^{- 1}$

Step 2.1.3

Add $3$ and $1$ .

${(\frac{r^{- 1} s^{2}}{r^{- 2} s^{0} t^{4}})}^{- 1}$

Step 2.2

Simplify $r^{- 2} s^{0} t^{4}$ .

${(\frac{r^{- 1} s^{2}}{r^{- 2} t^{4}})}^{- 1}$

Step 3

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

${(\frac{r^{- 1} s^{2} r^{2}}{t^{4}})}^{- 1}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $r^{- 1}$ by $r^{2}$ by adding the exponents.

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Step 4.1.1

Move $r^{2}$ .

${(\frac{r^{2} r^{- 1} s^{2}}{t^{4}})}^{- 1}$

Step 4.1.2

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

${(\frac{r^{2 - 1} s^{2}}{t^{4}})}^{- 1}$

Step 4.1.3

Subtract $1$ from $2$ .

${(\frac{r^{1} s^{2}}{t^{4}})}^{- 1}$

Step 4.2

Simplify $r^{1} s^{2}$ .

${(\frac{r s^{2}}{t^{4}})}^{- 1}$

Step 5

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{t^{4}}{r s^{2}}$