Basic Math Examples

${(a^{- 2} b^{4})}^{2} a^{5} b - 3$

Step 1

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

${(\frac{1}{a^{2}} b^{4})}^{2} a^{5} b - 3$

Step 2

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

${(\frac{b^{4}}{a^{2}})}^{2} a^{5} b - 3$

Step 3

Apply the product rule to $\frac{b^{4}}{a^{2}}$ .

$\frac{{(b^{4})}^{2}}{{(a^{2})}^{2}} a^{5} b - 3$

Step 4

Multiply the exponents in ${(b^{4})}^{2}$ .

Tap for more steps...

Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{b^{4 \cdot 2}}{{(a^{2})}^{2}} a^{5} b - 3$

Step 4.2

Multiply $4$ by $2$ .

$\frac{b^{8}}{{(a^{2})}^{2}} a^{5} b - 3$

Step 5

Multiply the exponents in ${(a^{2})}^{2}$ .

Tap for more steps...

Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{b^{8}}{a^{2 \cdot 2}} a^{5} b - 3$

Step 5.2

Multiply $2$ by $2$ .

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

Step 6

Cancel the common factor of $a^{4}$ .

Tap for more steps...

Step 6.1

Factor $a^{4}$ out of $a^{5}$ .

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

$b^{8} a b - 3$

Step 7

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

Tap for more steps...

Step 7.1

Move $b$ .

$b \cdot b^{8} a - 3$

Step 7.2

Multiply $b$ by $b^{8}$ .

Tap for more steps...

Step 7.2.1

Raise $b$ to the power of $1$ .

$b^{1} b^{8} a - 3$

Step 7.2.2

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

$b^{1 + 8} a - 3$

Step 7.3

Add $1$ and $8$ .

$b^{9} a - 3$