Basic Math Examples

$4 a^{- 3} {(- 4 a y)}^{2} {(- y)}^{- 3}$

Step 1

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

$4 \frac{1}{a^{3}} {(- 4 a y)}^{2} {(- y)}^{- 3}$

Step 2

Combine $4$ and $\frac{1}{a^{3}}$ .

$\frac{4}{a^{3}} {(- 4 a y)}^{2} {(- y)}^{- 3}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to $- 4 a y$ .

$\frac{4}{a^{3}} ({(- 4 a)}^{2} y^{2}) {(- y)}^{- 3}$

Step 3.2

Apply the product rule to $- 4 a$ .

$\frac{4}{a^{3}} ({(- 4)}^{2} a^{2} y^{2}) {(- y)}^{- 3}$

Step 4

Rewrite using the commutative property of multiplication.

${(- 4)}^{2} \frac{4}{a^{3}} (a^{2} y^{2}) {(- y)}^{- 3}$

Step 5

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

$16 \frac{4}{a^{3}} (a^{2} y^{2}) {(- y)}^{- 3}$

Step 6

Multiply $16 \frac{4}{a^{3}}$ .

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Step 6.1

Combine $16$ and $\frac{4}{a^{3}}$ .

$\frac{16 \cdot 4}{a^{3}} (a^{2} y^{2}) {(- y)}^{- 3}$

Step 6.2

Multiply $16$ by $4$ .

$\frac{64}{a^{3}} (a^{2} y^{2}) {(- y)}^{- 3}$

Step 7

Cancel the common factor of $a^{2}$ .

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Step 7.1

Factor $a^{2}$ out of $a^{3}$ .

$\frac{64}{a^{2} a} (a^{2} y^{2}) {(- y)}^{- 3}$

Step 7.2

Factor $a^{2}$ out of $a^{2} y^{2}$ .

$\frac{64}{a^{2} a} (a^{2} (y^{2})) {(- y)}^{- 3}$

Step 7.3

Cancel the common factor.

$\frac{64}{a^{2} a} (a^{2} y^{2}) {(- y)}^{- 3}$

Step 7.4

Rewrite the expression.

$\frac{64}{a} y^{2} {(- y)}^{- 3}$

Step 8

Combine $\frac{64}{a}$ and $y^{2}$ .

$\frac{64 y^{2}}{a} {(- y)}^{- 3}$

Step 9

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

$\frac{64 y^{2}}{a} \cdot \frac{1}{{(- y)}^{3}}$

Step 10

Combine.

$\frac{64 y^{2} \cdot 1}{a {(- y)}^{3}}$

Step 11

Cancel the common factor of $y^{2}$ and ${(- y)}^{3}$ .

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Step 11.1

Factor $- 1$ out of $y$ .

$\frac{64 {(- 1 (- y))}^{2} \cdot 1}{a {(- y)}^{3}}$

Step 11.2

Apply the product rule to $- 1 (- y)$ .

$\frac{64 ({(- 1)}^{2} {(- y)}^{2}) \cdot 1}{a {(- y)}^{3}}$

Step 11.3

Raise $- 1$ to the power of $2$ .

$\frac{64 (1 {(- y)}^{2}) \cdot 1}{a {(- y)}^{3}}$

Step 11.4

Multiply ${(- y)}^{2}$ by $1$ .

$\frac{64 {(- y)}^{2} \cdot 1}{a {(- y)}^{3}}$

Step 11.5

Factor ${(- y)}^{2}$ out of $64 {(- y)}^{2} \cdot 1$ .

$\frac{{(- y)}^{2} (64 \cdot 1)}{a {(- y)}^{3}}$

Step 11.6

Cancel the common factors.

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Step 11.6.1

Factor ${(- y)}^{2}$ out of $a {(- y)}^{3}$ .

$\frac{{(- y)}^{2} (64 \cdot 1)}{{(- y)}^{2} (a (- y))}$

Step 11.6.2

Cancel the common factor.

$\frac{{(- y)}^{2} (64 \cdot 1)}{{(- y)}^{2} (a (- y))}$

Step 11.6.3

Rewrite the expression.

$\frac{64 \cdot 1}{a (- y)}$

Step 12

Cancel the common factor of $1$ and $- 1$ .

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Step 12.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{64 \cdot (- 1 (- 1))}{a (- y)}$

Step 12.2

Move the negative in front of the fraction.

$- \frac{64}{a (y)}$

$- \frac{64}{a y}$