Basic Math Examples

$(5 a^{2}) (10 b^{3}) \div 2 a^{3} (25 b^{- 2})$

Step 1

Rewrite the division as a fraction.

$\frac{(5 a^{2}) (10 b^{3})}{2 a^{3} (25 b^{- 2})}$

Step 2

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

$\frac{(5 a^{2}) (10 b^{3}) b^{2}}{2 a^{3} \cdot 25}$

Step 3

Multiply $b^{3}$ by $b^{2}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $b^{2}$ .

$\frac{5 a^{2} (10 (b^{2} b^{3}))}{2 a^{3} \cdot 25}$

Step 3.2

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

$\frac{5 a^{2} (10 b^{2 + 3})}{2 a^{3} \cdot 25}$

Step 3.3

Add $2$ and $3$ .

$\frac{5 a^{2} (10 b^{5})}{2 a^{3} \cdot 25}$

Step 4

Cancel the common factor of $5$ and $25$ .

Tap for more steps...

Step 4.1

Factor $5$ out of $5 a^{2} (10 b^{5})$ .

$\frac{5 (a^{2} (10 b^{5}))}{2 a^{3} \cdot 25}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $5$ out of $2 a^{3} \cdot 25$ .

$\frac{5 (a^{2} (10 b^{5}))}{5 (2 a^{3} \cdot 5)}$

Step 4.2.2

Cancel the common factor.

$\frac{5 (a^{2} (10 b^{5}))}{5 (2 a^{3} \cdot 5)}$

Step 4.2.3

Rewrite the expression.

$\frac{a^{2} (10 b^{5})}{2 a^{3} \cdot 5}$

Step 5

Cancel the common factors.

Tap for more steps...

Step 5.1

Factor $a^{2}$ out of $2 a^{3} \cdot 5$ .

$\frac{a^{2} (10 b^{5})}{a^{2} (2 a \cdot 5)}$

Step 5.2

Cancel the common factor.

$\frac{a^{2} (10 b^{5})}{a^{2} (2 a \cdot 5)}$

Step 5.3

Rewrite the expression.

$\frac{10 b^{5}}{2 a \cdot 5}$

Step 6

Cancel the common factor of $10$ and $2$ .

Tap for more steps...

Step 6.1

Factor $2$ out of $10 b^{5}$ .

$\frac{2 (5 b^{5})}{2 a \cdot 5}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $2$ out of $2 a \cdot 5$ .

$\frac{2 (5 b^{5})}{2 (a \cdot 5)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (5 b^{5})}{2 (a \cdot 5)}$

Step 6.2.3

Rewrite the expression.

$\frac{5 b^{5}}{a \cdot 5}$

Step 7

Cancel the common factor of $5$ .

Tap for more steps...

Step 7.1

Cancel the common factor.

$\frac{5 b^{5}}{a \cdot 5}$

Step 7.2

Rewrite the expression.

$\frac{b^{5}}{a}$