Simplify ((2r^-1s^2t^0)^-2)/(2rs)

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

Step 1

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

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

Step 2

Simplify the denominator.

Apply the product rule to $2 r^{- 1} s^{2} t^{0}$ .

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

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

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

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

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

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

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

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

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

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

Apply the product rule to $2 s^{2}$ .

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

Simplify the numerator.

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

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

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

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

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

Multiply $2$ by $2$ .

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

Multiply the exponents in ${(t^{0})}^{2}$ .

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

$\frac{1}{2 r s \frac{4 s^{4}}{r^{2}} t^{0 \cdot 2}}$

Multiply $0$ by $2$ .

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

Anything raised to $0$ is $1$ .

$\frac{1}{2 r s \frac{4 s^{4}}{r^{2}} \cdot 1}$

Combine exponents.

Combine $2$ and $\frac{4 s^{4}}{r^{2}}$ .

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

Multiply $4$ by $2$ .

$\frac{1}{r s \frac{8 s^{4}}{r^{2}} \cdot 1}$

Combine $r$ and $\frac{8 s^{4}}{r^{2}}$ .

$\frac{1}{s \frac{r (8 s^{4})}{r^{2}} \cdot 1}$

Combine $s$ and $\frac{r (8 s^{4})}{r^{2}}$ .

$\frac{1}{\frac{s (r (8 s^{4}))}{r^{2}} \cdot 1}$

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

$\frac{1}{\frac{r (8 (s^{1} s^{4}))}{r^{2}} \cdot 1}$

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

$\frac{1}{\frac{r (8 s^{1 + 4})}{r^{2}} \cdot 1}$

Add $1$ and $4$ .

$\frac{1}{\frac{r (8 s^{5})}{r^{2}} \cdot 1}$

Multiply $\frac{r (8 s^{5})}{r^{2}}$ by $1$ .

$\frac{1}{\frac{r (8 s^{5})}{r^{2}}}$

Rewrite.

$\frac{1}{\frac{s (r (8 s^{4}))}{r^{2}}}$

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

$\frac{1}{\frac{r (8 (s^{1} s^{4}))}{r^{2}}}$

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

$\frac{1}{\frac{r (8 s^{1 + 4})}{r^{2}}}$

Add $1$ and $4$ .

$\frac{1}{\frac{r (8 s^{5})}{r^{2}}}$

Remove unnecessary parentheses.

$\frac{1}{\frac{r \cdot 8 s^{5}}{r^{2}}}$

Reduce the expression $\frac{r \cdot 8 s^{5}}{r^{2}}$ by cancelling the common factors.

Factor $r$ out of $r \cdot 8 s^{5}$ .

$\frac{1}{\frac{r (8 s^{5})}{r^{2}}}$

Factor $r$ out of $r^{2}$ .

$\frac{1}{\frac{r (8 s^{5})}{r \cdot r}}$

Cancel the common factor.

$\frac{1}{\frac{r (8 s^{5})}{r \cdot r}}$

Rewrite the expression.

$\frac{1}{\frac{8 s^{5}}{r}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{r}{8 s^{5}}$

Step 4

Multiply $\frac{r}{8 s^{5}}$ by $1$ .

$\frac{r}{8 s^{5}}$

Simplify ((2r^-1s^2t^0)^-2)/(2rs)

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