Basic Math Examples

$16 b^{3} \div 4 b^{- 5} \cdot (3 b^{- 1})$

Step 1

Rewrite using the commutative property of multiplication.

$3 16 b^{3} \div 4 b^{- 5} b^{- 1}$

Step 2

Rewrite the division as a fraction.

$3 \frac{16 b^{3}}{4 b^{- 5}} b^{- 1}$

Step 3

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

$3 \frac{16 b^{3} b^{5}}{4} b^{- 1}$

Step 4

Multiply $b^{3}$ by $b^{5}$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $b^{5}$ .

$3 \frac{16 (b^{5} b^{3})}{4} b^{- 1}$

Step 4.2

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

$3 \frac{16 b^{5 + 3}}{4} b^{- 1}$

Step 4.3

Add $5$ and $3$ .

$3 \frac{16 b^{8}}{4} b^{- 1}$

Step 5

Cancel the common factor of $16$ and $4$ .

Tap for more steps...

Step 5.1

Factor $4$ out of $16 b^{8}$ .

$3 \frac{4 (4 b^{8})}{4} b^{- 1}$

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $4$ out of $4$ .

$3 \frac{4 (4 b^{8})}{4 (1)} b^{- 1}$

Step 5.2.2

Cancel the common factor.

$3 \frac{4 (4 b^{8})}{4 \cdot 1} b^{- 1}$

Step 5.2.3

Rewrite the expression.

$3 \frac{4 b^{8}}{1} b^{- 1}$

Step 5.2.4

Divide $4 b^{8}$ by $1$ .

$3 (4 b^{8}) b^{- 1}$

Step 6

Multiply $b^{8}$ by $b^{- 1}$ by adding the exponents.

Tap for more steps...

Step 6.1

Move $b^{- 1}$ .

$3 (4 (b^{- 1} b^{8}))$

Step 6.2

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

$3 (4 b^{- 1 + 8})$

Step 6.3

Add $- 1$ and $8$ .

$3 (4 b^{7})$

Step 7

Multiply $4$ by $3$ .

$12 b^{7}$