Simplify ((a^(2-9))/(8a+24))÷((3-a)/8)

$\frac{a^{2 - 9}}{8 a + 24} \div \frac{3 - a}{8}$

To divide by a fraction, multiply by its reciprocal.

$\frac{a^{2 - 9}}{8 a + 24} \cdot \frac{8}{3 - a}$

Move $a^{2 - 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{(8 a + 24) a^{- (2 - 9)}} \cdot \frac{8}{3 - a}$

Simplify the denominator.

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Factor $8$ out of $8 a + 24$ .

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Factor $8$ out of $8 a$ .

$\frac{1}{(8 (a) + 24) a^{- (2 - 9)}} \cdot \frac{8}{3 - a}$

Factor $8$ out of $24$ .

$\frac{1}{(8 a + 8 \cdot 3) a^{- (2 - 9)}} \cdot \frac{8}{3 - a}$

Factor $8$ out of $8 a + 8 \cdot 3$ .

$\frac{1}{8 (a + 3) a^{- (2 - 9)}} \cdot \frac{8}{3 - a}$

Subtract $9$ from $2$ .

$\frac{1}{8 (a + 3) a^{- - 7}} \cdot \frac{8}{3 - a}$

Multiply $- 1$ by $- 7$ .

$\frac{1}{8 (a + 3) a^{7}} \cdot \frac{8}{3 - a}$

Simplify terms.

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Cancel the common factor of $8$ .

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Factor $8$ out of $8 (a + 3) a^{7}$ .

$\frac{1}{8 ((a + 3) a^{7})} \cdot \frac{8}{3 - a}$

Cancel the common factor.

$\frac{1}{8 ((a + 3) a^{7})} \cdot \frac{8}{3 - a}$

Rewrite the expression.

$\frac{1}{(a + 3) a^{7}} \cdot \frac{1}{3 - a}$

Multiply $\frac{1}{(a + 3) a^{7}}$ and $\frac{1}{3 - a}$ .

$\frac{1}{(a + 3) a^{7} (3 - a)}$

Reorder factors in $\frac{1}{(a + 3) a^{7} (3 - a)}$ .

$\frac{1}{a^{7} (a + 3) (3 - a)}$

Simplify ((a^(2-9))/(8a+24))÷((3-a)/8)

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