Simplify (24m^-2n)(1/4mn)

$(24 m^{- 2} n) (\frac{1}{4} m n)$

Step 1

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

Move $m$ .

$24 (m \cdot m^{- 2}) n (\frac{1}{4} \cdot (n))$

Multiply $m$ by $m^{- 2}$ .

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

$24 (m^{1} m^{- 2}) n (\frac{1}{4} \cdot (n))$

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

$24 m^{1 - 2} n (\frac{1}{4} \cdot (n))$

Subtract $2$ from $1$ .

$24 m^{- 1} n (\frac{1}{4} \cdot (n))$

Step 2

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

$24 m^{- 1} (n \cdot n) \frac{1}{4}$

Multiply $n$ by $n$ .

$24 m^{- 1} n^{2} \frac{1}{4}$

Step 3

Cancel the common factor of $4$ .

Factor $4$ out of $24 m^{- 1} n^{2}$ .

$4 (6 m^{- 1} n^{2}) \frac{1}{4}$

Cancel the common factor.

$4 (6 m^{- 1} n^{2}) \frac{1}{4}$

Rewrite the expression.

$6 m^{- 1} n^{2}$

Step 4

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

$6 \frac{1}{m} n^{2}$

Step 5

Combine $6$ and $\frac{1}{m}$ .

$\frac{6}{m} n^{2}$

Step 6

Combine $\frac{6}{m}$ and $n^{2}$ .

$\frac{6 n^{2}}{m}$