Basic Math Examples

$24 b^{- 1} \div 8 b^{- 7}$

Step 1

Rewrite the division as a fraction.

$\frac{24 b^{- 1}}{8 b^{- 7}}$

Step 2

Move $b^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{24 b^{- 1} b^{7}}{8}$

Step 3

Multiply $b^{- 1}$ by $b^{7}$ by adding the exponents.

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Step 3.1

Move $b^{7}$ .

$\frac{24 (b^{7} b^{- 1})}{8}$

Step 3.2

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

$\frac{24 b^{7 - 1}}{8}$

Step 3.3

Subtract $1$ from $7$ .

$\frac{24 b^{6}}{8}$

Step 4

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

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Step 4.1

Factor $8$ out of $24 b^{6}$ .

$\frac{8 (3 b^{6})}{8}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $8$ out of $8$ .

$\frac{8 (3 b^{6})}{8 (1)}$

Step 4.2.2

Cancel the common factor.

$\frac{8 (3 b^{6})}{8 \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{3 b^{6}}{1}$

Step 4.2.4

Divide $3 b^{6}$ by $1$ .

$3 b^{6}$