Pre-Algebra Examples

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

Step 1

Move $b^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

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

Tap for more steps...

Step 2.1

Move $b^{3}$ .

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

Step 2.2

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

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

Step 2.3

Add $3$ and $5$ .

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

Step 3

Cancel the common factor of $a^{5}$ and $a^{3}$ .

Tap for more steps...

Step 3.1

Factor $a^{3}$ out of $a^{5}$ .

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

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $a^{3}$ out of $a^{3} b^{8}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 5

Apply the product rule to $\frac{b^{8}}{a^{2}}$ .

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

Step 6

Multiply the exponents in ${(b^{8})}^{5}$ .

Tap for more steps...

Step 6.1

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

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

Step 6.2

Multiply $8$ by $5$ .

$\frac{b^{40}}{{(a^{2})}^{5}}$

Step 7

Multiply the exponents in ${(a^{2})}^{5}$ .

Tap for more steps...

Step 7.1

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

$\frac{b^{40}}{a^{2 \cdot 5}}$

Step 7.2

Multiply $2$ by $5$ .

$\frac{b^{40}}{a^{10}}$