Algebra Examples

$4 z^{a + 2} \div (- 8 z^{a - 2})$

Step 1

Rewrite the division as a fraction.

$\frac{4 z^{a + 2}}{- 8 z^{a - 2}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

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

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Step 2.1.1

Factor $4$ out of $4 z^{a + 2}$ .

$\frac{4 (z^{a + 2})}{- 8 z^{a - 2}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $4$ out of $- 8 z^{a - 2}$ .

$\frac{4 (z^{a + 2})}{4 (- 2 z^{a - 2})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{4 z^{a + 2}}{4 (- 2 z^{a - 2})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{z^{a + 2}}{- 2 z^{a - 2}}$

Step 2.2

Cancel the common factor of $z^{a + 2}$ and $z^{a - 2}$ .

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Step 2.2.1

Factor $z^{a - 2}$ out of $z^{a + 2}$ .

$\frac{z^{a - 2} z^{a + 2 - (a - 2)}}{- 2 z^{a - 2}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $z^{a - 2}$ out of $- 2 z^{a - 2}$ .

$\frac{z^{a - 2} z^{a + 2 - (a - 2)}}{z^{a - 2} \cdot - 2}$

Step 2.2.2.2

Cancel the common factor.

$\frac{z^{a - 2} z^{a + 2 - (a - 2)}}{z^{a - 2} \cdot - 2}$

Step 2.2.2.3

Rewrite the expression.

$\frac{z^{a + 2 - (a - 2)}}{- 2}$

Step 3

Simplify the numerator.

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$\frac{z^{a + 2 - a - - 2}}{- 2}$

Step 3.1.2

Multiply $- 1$ by $- 2$ .

$\frac{z^{a + 2 - a + 2}}{- 2}$

Step 3.2

Combine the opposite terms in $a + 2 - a + 2$ .

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Step 3.2.1

Subtract $a$ from $a$ .

$\frac{z^{0 + 2 + 2}}{- 2}$

Step 3.2.2

Add $0$ and $2$ .

$\frac{z^{2 + 2}}{- 2}$

Step 3.3

Add $2$ and $2$ .

$\frac{z^{4}}{- 2}$

Step 4

Move the negative in front of the fraction.

$- \frac{z^{4}}{2}$