Simplify (3x^9*y^-4)(6x^-8y^4)

$(3 x^{9} \cdot y^{- 4}) (6 x^{- 8} y^{4})$

Step 1

Multiply $x^{9}$ by $x^{- 8}$ by adding the exponents.

Move $x^{- 8}$ .

$3 (x^{- 8} x^{9}) \cdot y^{- 4} (6 y^{4})$

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

$3 x^{- 8 + 9} \cdot y^{- 4} (6 y^{4})$

Add $- 8$ and $9$ .

$3 x^{1} \cdot y^{- 4} (6 y^{4})$

Step 2

Simplify $3 x^{1} \cdot y^{- 4} (6 y^{4})$ .

$3 x \cdot y^{- 4} (6 y^{4})$

Step 3

Multiply $y^{- 4}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$3 x \cdot (y^{4} y^{- 4}) \cdot 6$

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

$3 x \cdot y^{4 - 4} \cdot 6$

Subtract $4$ from $4$ .

$3 x \cdot y^{0} \cdot 6$

Step 4

Simplify $3 x \cdot y^{0} \cdot 6$ .

$3 x \cdot 6$

Step 5

Multiply $6$ by $3$ .

$18 x$