Algebra Examples

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

Step 1

Move ${(3 r^{- 2} s^{3} t^{0})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $3 r^{- 2} s^{3} t^{0}$ .

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

Step 2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2.3

Combine $3$ and $\frac{1}{r^{2}}$ .

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

Step 2.4

Combine $\frac{3}{r^{2}}$ and $s^{3}$ .

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

Step 2.5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 2.5.1

Apply the product rule to $\frac{3 s^{3}}{r^{2}}$ .

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

Step 2.5.2

Apply the product rule to $3 s^{3}$ .

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

Step 2.6

Simplify the numerator.

Tap for more steps...

Step 2.6.1

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

$\frac{1}{3 r s \frac{27 {(s^{3})}^{3}}{{(r^{2})}^{3}} {(t^{0})}^{3}}$

Step 2.6.2

Multiply the exponents in ${(s^{3})}^{3}$ .

Tap for more steps...

Step 2.6.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{3 r s \frac{27 s^{3 \cdot 3}}{{(r^{2})}^{3}} {(t^{0})}^{3}}$

Step 2.6.2.2

Multiply $3$ by $3$ .

$\frac{1}{3 r s \frac{27 s^{9}}{{(r^{2})}^{3}} {(t^{0})}^{3}}$

Step 2.7

Multiply the exponents in ${(r^{2})}^{3}$ .

Tap for more steps...

Step 2.7.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{3 r s \frac{27 s^{9}}{r^{2 \cdot 3}} {(t^{0})}^{3}}$

Step 2.7.2

Multiply $2$ by $3$ .

$\frac{1}{3 r s \frac{27 s^{9}}{r^{6}} {(t^{0})}^{3}}$

Step 2.8

Multiply the exponents in ${(t^{0})}^{3}$ .

Tap for more steps...

Step 2.8.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{3 r s \frac{27 s^{9}}{r^{6}} t^{0 \cdot 3}}$

Step 2.8.2

Multiply $0$ by $3$ .

$\frac{1}{3 r s \frac{27 s^{9}}{r^{6}} t^{0}}$

Step 2.9

Anything raised to $0$ is $1$ .

$\frac{1}{3 r s \frac{27 s^{9}}{r^{6}} \cdot 1}$

Step 2.10

Combine exponents.

Tap for more steps...

Step 2.10.1

Combine $3$ and $\frac{27 s^{9}}{r^{6}}$ .

$\frac{1}{r s \frac{3 (27 s^{9})}{r^{6}} \cdot 1}$

Step 2.10.2

Multiply $27$ by $3$ .

$\frac{1}{r s \frac{81 s^{9}}{r^{6}} \cdot 1}$

Step 2.10.3

Combine $r$ and $\frac{81 s^{9}}{r^{6}}$ .

$\frac{1}{s \frac{r (81 s^{9})}{r^{6}} \cdot 1}$

Step 2.10.4

Combine $s$ and $\frac{r (81 s^{9})}{r^{6}}$ .

$\frac{1}{\frac{s (r (81 s^{9}))}{r^{6}} \cdot 1}$

Step 2.10.5

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

$\frac{1}{\frac{r (81 (s^{1} s^{9}))}{r^{6}} \cdot 1}$

Step 2.10.6

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

$\frac{1}{\frac{r (81 s^{1 + 9})}{r^{6}} \cdot 1}$

Step 2.10.7

Add $1$ and $9$ .

$\frac{1}{\frac{r (81 s^{10})}{r^{6}} \cdot 1}$

Step 2.10.8

Multiply $\frac{r (81 s^{10})}{r^{6}}$ by $1$ .

$\frac{1}{\frac{r (81 s^{10})}{r^{6}}}$

Step 2.11

Rewrite.

$\frac{1}{\frac{s (r (81 s^{9}))}{r^{6}}}$

Step 2.12

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

$\frac{1}{\frac{r (81 (s^{1} s^{9}))}{r^{6}}}$

Step 2.13

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

$\frac{1}{\frac{r (81 s^{1 + 9})}{r^{6}}}$

Step 2.14

Add $1$ and $9$ .

$\frac{1}{\frac{r (81 s^{10})}{r^{6}}}$

Step 2.15

Remove unnecessary parentheses.

$\frac{1}{\frac{r \cdot 81 s^{10}}{r^{6}}}$

Step 2.16

Reduce the expression $\frac{r \cdot 81 s^{10}}{r^{6}}$ by cancelling the common factors.

Tap for more steps...

Step 2.16.1

Factor $r$ out of $r \cdot 81 s^{10}$ .

$\frac{1}{\frac{r (81 s^{10})}{r^{6}}}$

Step 2.16.2

Factor $r$ out of $r^{6}$ .

$\frac{1}{\frac{r (81 s^{10})}{r \cdot r^{5}}}$

Step 2.16.3

Cancel the common factor.

$\frac{1}{\frac{r (81 s^{10})}{r \cdot r^{5}}}$

Step 2.16.4

Rewrite the expression.

$\frac{1}{\frac{81 s^{10}}{r^{5}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{r^{5}}{81 s^{10}}$

Step 4

Multiply $\frac{r^{5}}{81 s^{10}}$ by $1$ .

$\frac{r^{5}}{81 s^{10}}$