Simplify ((4m^2n^-3)^2*12n^13)/(8m^20)

$\frac{{(4 m^{2} n^{- 3})}^{2} \cdot 12 n^{13}}{8 m^{20}}$

Step 1

Cancel the common factor of $12$ and $8$ .

Factor $4$ out of ${(4 m^{2} n^{- 3})}^{2} \cdot (12 n^{13})$ .

$\frac{4 ({(4 m^{2} n^{- 3})}^{2} \cdot (3 n^{13}))}{8 m^{20}}$

Cancel the common factors.

Factor $4$ out of $8 m^{20}$ .

$\frac{4 ({(4 m^{2} n^{- 3})}^{2} \cdot (3 n^{13}))}{4 (2 m^{20})}$

Cancel the common factor.

$\frac{4 ({(4 m^{2} n^{- 3})}^{2} \cdot (3 n^{13}))}{4 (2 m^{20})}$

Rewrite the expression.

$\frac{{(4 m^{2} n^{- 3})}^{2} \cdot (3 n^{13})}{2 m^{20}}$

Step 2

Simplify the numerator.

Apply the product rule to $4 m^{2} n^{- 3}$ .

$\frac{{(4 m^{2})}^{2} {(n^{- 3})}^{2} \cdot 3 n^{13}}{2 m^{20}}$

Apply the product rule to $4 m^{2}$ .

$\frac{4^{2} {(m^{2})}^{2} {(n^{- 3})}^{2} \cdot 3 n^{13}}{2 m^{20}}$

Raise $4$ to the power of $2$ .

$\frac{16 {(m^{2})}^{2} {(n^{- 3})}^{2} \cdot 3 n^{13}}{2 m^{20}}$

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

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

$\frac{16 m^{2 \cdot 2} {(n^{- 3})}^{2} \cdot 3 n^{13}}{2 m^{20}}$

Multiply $2$ by $2$ .

$\frac{16 m^{4} {(n^{- 3})}^{2} \cdot 3 n^{13}}{2 m^{20}}$

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

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

$\frac{16 m^{4} n^{- 3 \cdot 2} \cdot 3 n^{13}}{2 m^{20}}$

Multiply $- 3$ by $2$ .

$\frac{16 m^{4} n^{- 6} \cdot 3 n^{13}}{2 m^{20}}$

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

$\frac{16 m^{4} \frac{1}{n^{6}} \cdot 3 n^{13}}{2 m^{20}}$

Combine exponents.

Combine $16$ and $\frac{1}{n^{6}}$ .

$\frac{m^{4} \frac{16}{n^{6}} \cdot 3 n^{13}}{2 m^{20}}$

Combine $m^{4}$ and $\frac{16}{n^{6}}$ .

$\frac{\frac{m^{4} \cdot 16}{n^{6}} \cdot 3 n^{13}}{2 m^{20}}$

Combine $\frac{m^{4} \cdot 16}{n^{6}}$ and $3$ .

$\frac{\frac{m^{4} \cdot 16 \cdot 3}{n^{6}} n^{13}}{2 m^{20}}$

Multiply $3$ by $16$ .

$\frac{\frac{m^{4} \cdot 48}{n^{6}} n^{13}}{2 m^{20}}$

Combine $\frac{m^{4} \cdot 48}{n^{6}}$ and $n^{13}$ .

$\frac{\frac{m^{4} \cdot 48 n^{13}}{n^{6}}}{2 m^{20}}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{m^{4} \cdot 48 n^{13}}{n^{6}}$ by cancelling the common factors.

Factor $n^{6}$ out of $m^{4} \cdot 48 n^{13}$ .

$\frac{\frac{n^{6} (m^{4} \cdot 48 n^{7})}{n^{6}}}{2 m^{20}}$

Multiply by $1$ .

$\frac{\frac{n^{6} (m^{4} \cdot 48 n^{7})}{n^{6} \cdot 1}}{2 m^{20}}$

Cancel the common factor.

$\frac{\frac{n^{6} (m^{4} \cdot 48 n^{7})}{n^{6} \cdot 1}}{2 m^{20}}$

Rewrite the expression.

$\frac{\frac{m^{4} \cdot 48 n^{7}}{1}}{2 m^{20}}$

Divide $m^{4} \cdot 48 n^{7}$ by $1$ .

$\frac{m^{4} \cdot 48 n^{7}}{2 m^{20}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $m^{4}$ and $m^{20}$ .

Factor $m^{4}$ out of $m^{4} \cdot 48 n^{7}$ .

$\frac{m^{4} (48 n^{7})}{2 m^{20}}$

Cancel the common factors.

Factor $m^{4}$ out of $2 m^{20}$ .

$\frac{m^{4} (48 n^{7})}{m^{4} (2 m^{16})}$

Cancel the common factor.

$\frac{m^{4} (48 n^{7})}{m^{4} (2 m^{16})}$

Rewrite the expression.

$\frac{48 n^{7}}{2 m^{16}}$

Cancel the common factor of $48$ and $2$ .

Factor $2$ out of $48 n^{7}$ .

$\frac{2 (24 n^{7})}{2 m^{16}}$

Cancel the common factors.

Factor $2$ out of $2 m^{16}$ .

$\frac{2 (24 n^{7})}{2 (m^{16})}$

Cancel the common factor.

$\frac{2 (24 n^{7})}{2 m^{16}}$

Rewrite the expression.

$\frac{24 n^{7}}{m^{16}}$

Simplify ((4m^2n^-3)^2*12n^13)/(8m^20)

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