Simplify ((8k^-5)(2k^3))/(4k^-6)

$\frac{(8 k^{- 5}) (2 k^{3})}{4 k^{- 6}}$

Step 1

Multiply $k^{- 5}$ by $k^{3}$ by adding the exponents.

Move $k^{3}$ .

$\frac{8 (k^{3} k^{- 5}) \cdot 2}{4 k^{- 6}}$

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

$\frac{8 k^{3 - 5} \cdot 2}{4 k^{- 6}}$

Subtract $5$ from $3$ .

$\frac{8 k^{- 2} \cdot 2}{4 k^{- 6}}$

Step 2

Move $k^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{8 k^{- 2} \cdot 2 k^{6}}{4}$

Step 3

Multiply $k^{- 2}$ by $k^{6}$ by adding the exponents.

Move $k^{6}$ .

$\frac{8 (k^{6} k^{- 2}) \cdot 2}{4}$

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

$\frac{8 k^{6 - 2} \cdot 2}{4}$

Subtract $2$ from $6$ .

$\frac{8 k^{4} \cdot 2}{4}$

Step 4

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $8 k^{4} \cdot 2$ .

$\frac{4 (2 k^{4} \cdot 2)}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 k^{4} \cdot 2}{1}$

Divide $2 k^{4} \cdot 2$ by $1$ .

$2 k^{4} \cdot 2$

Step 5

Multiply $2$ by $2$ .

$4 k^{4}$