Algebra Examples

$x^{- 4} y^{4} z^{2} \cdot 4 x^{3} y^{0} z^{- 2}$

Step 1

Rewrite using the commutative property of multiplication.

$4 x^{- 4} y^{4} z^{2} (x^{3} y^{0} z^{- 2})$

Step 2

Multiply $x^{- 4}$ by $x^{3}$ by adding the exponents.

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Step 2.1

Move $x^{3}$ .

$4 (x^{3} x^{- 4}) y^{4} z^{2} (y^{0} z^{- 2})$

Step 2.2

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

$4 x^{3 - 4} y^{4} z^{2} (y^{0} z^{- 2})$

Step 2.3

Subtract $4$ from $3$ .

$4 x^{- 1} y^{4} z^{2} (y^{0} z^{- 2})$

Step 3

Simplify $4 x^{- 1} y^{4} z^{2} (y^{0} z^{- 2})$ .

$4 x^{- 1} y^{4} z^{2} z^{- 2}$

Step 4

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

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Step 4.1

Move $z^{- 2}$ .

$4 x^{- 1} y^{4} (z^{- 2} z^{2})$

Step 4.2

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

$4 x^{- 1} y^{4} z^{- 2 + 2}$

Step 4.3

Add $- 2$ and $2$ .

$4 x^{- 1} y^{4} z^{0}$

Step 5

Simplify $4 x^{- 1} y^{4} z^{0}$ .

$4 x^{- 1} y^{4}$

Step 6

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

$4 \frac{1}{x} y^{4}$

Step 7

Combine $4$ and $\frac{1}{x}$ .

$\frac{4}{x} y^{4}$

Step 8

Combine $\frac{4}{x}$ and $y^{4}$ .

$\frac{4 y^{4}}{x}$