Basic Math Examples

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

Step 1

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

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

Step 2

Multiply $a^{4}$ by $a^{3}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $a^{3}$ .

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

Step 2.2

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

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

Step 2.3

Add $3$ and $4$ .

${(\frac{b^{5}}{a^{7} b^{- 2}})}^{- 3}$

Step 3

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

${(\frac{b^{5} b^{2}}{a^{7}})}^{- 3}$

Step 4

Multiply $b^{5}$ by $b^{2}$ by adding the exponents.

Tap for more steps...

Step 4.1

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

${(\frac{b^{5 + 2}}{a^{7}})}^{- 3}$

Step 4.2

Add $5$ and $2$ .

${(\frac{b^{7}}{a^{7}})}^{- 3}$

Step 5

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

${(\frac{a^{7}}{b^{7}})}^{3}$

Step 6

Apply the product rule to $\frac{a^{7}}{b^{7}}$ .

$\frac{{(a^{7})}^{3}}{{(b^{7})}^{3}}$

Step 7

Multiply the exponents in ${(a^{7})}^{3}$ .

Tap for more steps...

Step 7.1

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

$\frac{a^{7 \cdot 3}}{{(b^{7})}^{3}}$

Step 7.2

Multiply $7$ by $3$ .

$\frac{a^{21}}{{(b^{7})}^{3}}$

Step 8

Multiply the exponents in ${(b^{7})}^{3}$ .

Tap for more steps...

Step 8.1

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

$\frac{a^{21}}{b^{7 \cdot 3}}$

Step 8.2

Multiply $7$ by $3$ .

$\frac{a^{21}}{b^{21}}$