Simplify 8a^2(2a^-7)(4w^-7y^-2y^3w)

$8 a^{2} \cdot (2 a^{- 7}) \cdot (4 w^{- 7} y^{- 2} y^{3} w)$

Step 1

Multiply

$a^{2}$ by

$a^{- 7}$ by adding the exponents.

Move

$a^{- 7}$ .

$8 (a^{- 7} a^{2}) \cdot 2 \cdot (4 w^{- 7} y^{- 2} y^{3} w)$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 a^{- 7 + 2} \cdot 2 \cdot (4 w^{- 7} y^{- 2} y^{3} w)$

Add

$- 7$ and

$2$ .

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 7} y^{- 2} y^{3} w)$

Step 2

Multiply

$w^{- 7}$ by

$w$ by adding the exponents.

Move

$w$ .

$8 a^{- 5} \cdot 2 \cdot (4 (w \cdot w^{- 7}) y^{- 2} y^{3})$

Multiply

$w$ by

$w^{- 7}$ .

Raise

$w$ to the power of

$1$ .

$8 a^{- 5} \cdot 2 \cdot (4 (w^{1} w^{- 7}) y^{- 2} y^{3})$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 a^{- 5} \cdot 2 \cdot (4 w^{1 - 7} y^{- 2} y^{3})$

Subtract

$7$ from

$1$ .

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} y^{- 2} y^{3})$

Step 3

Multiply

$y^{- 2}$ by

$y^{3}$ by adding the exponents.

Move

$y^{3}$ .

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} (y^{3} y^{- 2}))$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} y^{3 - 2})$

Subtract

$2$ from

$3$ .

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} y^{1})$

Step 4

Simplify

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} y^{1})$ .

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} y)$

Step 5

Rewrite the expression using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

$8 \frac{1}{a^{5}} \cdot 2 \cdot (4 w^{- 6} y)$

Step 6

Combine

$8$ and

$\frac{1}{a^{5}}$ .

$\frac{8}{a^{5}} \cdot 2 \cdot (4 w^{- 6} y)$

Step 7

Multiply

$\frac{8}{a^{5}} \cdot 2$ .

Combine

$\frac{8}{a^{5}}$ and

$2$ .

$\frac{8 \cdot 2}{a^{5}} \cdot (4 w^{- 6} y)$

Multiply

$8$ by

$2$ .

$\frac{16}{a^{5}} \cdot (4 w^{- 6} y)$

Step 8

Rewrite using the commutative property of multiplication.

$4 \frac{16}{a^{5}} w^{- 6} y$

Step 9

Multiply

$4 \frac{16}{a^{5}}$ .

Combine

$4$ and

$\frac{16}{a^{5}}$ .

$\frac{4 \cdot 16}{a^{5}} w^{- 6} y$

Multiply

$4$ by

$16$ .

$\frac{64}{a^{5}} w^{- 6} y$

Step 10

Rewrite the expression using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

$\frac{64}{a^{5}} \cdot \frac{1}{w^{6}} y$

Step 11

Combine.

$\frac{64 \cdot 1}{a^{5} w^{6}} y$

Step 12

Multiply

$64$ by

$1$ .

$\frac{64}{a^{5} w^{6}} y$

Step 13

Combine

$\frac{64}{a^{5} w^{6}}$ and

$y$ .

$\frac{64 y}{a^{5} w^{6}}$

Simplify 8a^2*(2a^-7)*(4w^-7y^-2y^3w)

Related Questions

Simplify 8a^2(2a^-7)(4w^-7y^-2y^3w)