Basic Math Examples

$- 8 a^{- 7} y^{- 5} \div 24 a^{- 10} b^{4}$

Step 1

Rewrite the division as a fraction.

$\frac{- 8 a^{- 7} y^{- 5}}{24 a^{- 10} b^{4}}$

Step 2

Move $y^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 8 a^{- 7}}{24 a^{- 10} b^{4} y^{5}}$

Step 3

Move $a^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 8 a^{- 7} a^{10}}{24 b^{4} y^{5}}$

Step 4

Multiply $a^{- 7}$ by $a^{10}$ by adding the exponents.

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Step 4.1

Move $a^{10}$ .

$\frac{- 8 (a^{10} a^{- 7})}{24 b^{4} y^{5}}$

Step 4.2

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

$\frac{- 8 a^{10 - 7}}{24 b^{4} y^{5}}$

Step 4.3

Subtract $7$ from $10$ .

$\frac{- 8 a^{3}}{24 b^{4} y^{5}}$

Step 5

Cancel the common factor of $- 8$ and $24$ .

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Step 5.1

Factor $8$ out of $- 8 a^{3}$ .

$\frac{8 (- a^{3})}{24 b^{4} y^{5}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $8$ out of $24 b^{4} y^{5}$ .

$\frac{8 (- a^{3})}{8 (3 b^{4} y^{5})}$

Step 5.2.2

Cancel the common factor.

$\frac{8 (- a^{3})}{8 (3 b^{4} y^{5})}$

Step 5.2.3

Rewrite the expression.

$\frac{- a^{3}}{3 b^{4} y^{5}}$

Step 6

Move the negative in front of the fraction.

$- \frac{a^{3}}{3 b^{4} y^{5}}$