Write the Fraction in Simplest Form (5(m^-2)^3)/(20m^9)

$\frac{5 {(m^{- 2})}^{3}}{20 m^{9}}$

Step 1

Cancel the common factor of $5$ and $20$ .

Factor $5$ out of $5 {(m^{- 2})}^{3}$ .

$\frac{5 ({(m^{- 2})}^{3})}{20 m^{9}}$

Cancel the common factors.

Factor $5$ out of $20 m^{9}$ .

$\frac{5 ({(m^{- 2})}^{3})}{5 (4 m^{9})}$

Cancel the common factor.

$\frac{5 {(m^{- 2})}^{3}}{5 (4 m^{9})}$

Rewrite the expression.

$\frac{{(m^{- 2})}^{3}}{4 m^{9}}$

Step 2

Simplify the numerator.

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

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

$\frac{m^{- 2 \cdot 3}}{4 m^{9}}$

Multiply $- 2$ by $3$ .

$\frac{m^{- 6}}{4 m^{9}}$

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

$\frac{\frac{1}{m^{6}}}{4 m^{9}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{m^{6}} \cdot \frac{1}{4 m^{9}}$

Step 4

Combine.

$\frac{1 \cdot 1}{m^{6} (4 m^{9})}$

Step 5

Multiply $m^{6}$ by $m^{9}$ by adding the exponents.

Move $m^{9}$ .

$\frac{1 \cdot 1}{m^{9} m^{6} \cdot 4}$

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

$\frac{1 \cdot 1}{m^{9 + 6} \cdot 4}$

Add $9$ and $6$ .

$\frac{1 \cdot 1}{m^{15} \cdot 4}$

Step 6

Multiply $1$ by $1$ .

$\frac{1}{m^{15} \cdot 4}$

Step 7

Move $4$ to the left of $m^{15}$ .

$\frac{1}{4 m^{15}}$