Basic Math Examples

$- a^{2^{b^{- 2}}} \div \frac{a^{- 2 b^{8}}}{a^{4 b^{- 2}}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$- a^{2^{b^{- 2}}} \frac{a^{4 b^{- 2}}}{a^{- 2 b^{8}}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- a^{2^{\frac{1}{b^{2}}}} \frac{a^{4 b^{- 2}}}{a^{- 2 b^{8}}}$

Step 3

Cancel the common factor of $a^{4 b^{- 2}}$ and $a^{- 2 b^{8}}$ .

Tap for more steps...

Step 3.1

Factor $a^{- 2 b^{8}}$ out of $a^{4 b^{- 2}}$ .

$- a^{2^{\frac{1}{b^{2}}}} \frac{a^{- 2 b^{8}} a^{4 b^{- 2} + 2 b^{8}}}{a^{- 2 b^{8}}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Multiply by $1$ .

$- a^{2^{\frac{1}{b^{2}}}} \frac{a^{- 2 b^{8}} a^{4 b^{- 2} + 2 b^{8}}}{a^{- 2 b^{8}} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$- a^{2^{\frac{1}{b^{2}}}} \frac{a^{- 2 b^{8}} a^{4 b^{- 2} + 2 b^{8}}}{a^{- 2 b^{8}} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$- a^{2^{\frac{1}{b^{2}}}} \frac{a^{4 b^{- 2} + 2 b^{8}}}{1}$

Step 3.2.4

Divide $a^{4 b^{- 2} + 2 b^{8}}$ by $1$ .

$- a^{2^{\frac{1}{b^{2}}}} a^{4 b^{- 2} + 2 b^{8}}$

Step 4

Multiply $a^{2^{\frac{1}{b^{2}}}}$ by $a^{4 b^{- 2} + 2 b^{8}}$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $a^{4 b^{- 2} + 2 b^{8}}$ .

$- (a^{4 b^{- 2} + 2 b^{8}} a^{2^{\frac{1}{b^{2}}}})$

Step 4.2

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

$- a^{4 b^{- 2} + 2 b^{8} + 2^{\frac{1}{b^{2}}}}$

Step 4.3

Simplify each term.

Tap for more steps...

Step 4.3.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- a^{4 \frac{1}{b^{2}} + 2 b^{8} + 2^{\frac{1}{b^{2}}}}$

Step 4.3.2

Combine $4$ and $\frac{1}{b^{2}}$ .

$- a^{\frac{4}{b^{2}} + 2 b^{8} + 2^{\frac{1}{b^{2}}}}$

Step 5

To write $2 b^{8}$ as a fraction with a common denominator, multiply by $\frac{b^{2}}{b^{2}}$ .

$- a^{\frac{4}{b^{2}} + \frac{2 b^{8} b^{2}}{b^{2}} + 2^{\frac{1}{b^{2}}}}$

Step 6

Combine the numerators over the common denominator.

$- a^{\frac{4 + 2 b^{8} b^{2}}{b^{2}} + 2^{\frac{1}{b^{2}}}}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Multiply $b^{8}$ by $b^{2}$ by adding the exponents.

Tap for more steps...

Step 7.1.1

Move $b^{2}$ .

$- a^{\frac{4 + 2 (b^{2} b^{8})}{b^{2}} + 2^{\frac{1}{b^{2}}}}$

Step 7.1.2

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

$- a^{\frac{4 + 2 b^{2 + 8}}{b^{2}} + 2^{\frac{1}{b^{2}}}}$

Step 7.1.3

Add $2$ and $8$ .

$- a^{\frac{4 + 2 b^{10}}{b^{2}} + 2^{\frac{1}{b^{2}}}}$

Step 7.2

Factor $2$ out of $4 + 2 b^{10}$ .

Tap for more steps...

Step 7.2.1

Factor $2$ out of $4$ .

$- a^{\frac{2 \cdot 2 + 2 b^{10}}{b^{2}} + 2^{\frac{1}{b^{2}}}}$

Step 7.2.2

Factor $2$ out of $2 \cdot 2 + 2 b^{10}$ .

$- a^{\frac{2 (2 + b^{10})}{b^{2}} + 2^{\frac{1}{b^{2}}}}$

Step 8

To write $2^{\frac{1}{b^{2}}}$ as a fraction with a common denominator, multiply by $\frac{b^{2}}{b^{2}}$ .

$- a^{\frac{2 (2 + b^{10})}{b^{2}} + \frac{2^{\frac{1}{b^{2}}} b^{2}}{b^{2}}}$

Step 9

Combine the numerators over the common denominator.

$- a^{\frac{2 (2 + b^{10}) + 2^{\frac{1}{b^{2}}} b^{2}}{b^{2}}}$

Step 10

Simplify the numerator.

Tap for more steps...

Step 10.1

Apply the distributive property.

$- a^{\frac{2 \cdot 2 + 2 b^{10} + 2^{\frac{1}{b^{2}}} b^{2}}{b^{2}}}$

Step 10.2

Multiply $2$ by $2$ .

$- a^{\frac{4 + 2 b^{10} + 2^{\frac{1}{b^{2}}} b^{2}}{b^{2}}}$

Step 10.3

Reorder terms.

$- a^{\frac{2 b^{10} + 2^{\frac{1}{b^{2}}} b^{2} + 4}{b^{2}}}$

Step 11

Reorder factors in $- a^{\frac{2 b^{10} + 2^{\frac{1}{b^{2}}} b^{2} + 4}{b^{2}}}$ .

$- a^{\frac{2 b^{10} + b^{2} \cdot 2^{\frac{1}{b^{2}}} + 4}{b^{2}}}$