Basic Math Examples

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

Step 1

Move $a^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Multiply $a^{2}$ by $a^{4}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $a^{4}$ .

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

Step 2.2

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

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

Step 2.3

Add $4$ and $2$ .

${(\frac{3}{4 a^{6}})}^{- 3}$

Step 3

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

${(\frac{4 a^{6}}{3})}^{3}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 4.1

Apply the product rule to $\frac{4 a^{6}}{3}$ .

$\frac{{(4 a^{6})}^{3}}{3^{3}}$

Step 4.2

Apply the product rule to $4 a^{6}$ .

$\frac{4^{3} {(a^{6})}^{3}}{3^{3}}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Raise $4$ to the power of $3$ .

$\frac{64 {(a^{6})}^{3}}{3^{3}}$

Step 5.2

Multiply the exponents in ${(a^{6})}^{3}$ .

Tap for more steps...

Step 5.2.1

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

$\frac{64 a^{6 \cdot 3}}{3^{3}}$

Step 5.2.2

Multiply $6$ by $3$ .

$\frac{64 a^{18}}{3^{3}}$

Step 6

Raise $3$ to the power of $3$ .

$\frac{64 a^{18}}{27}$