Algebra Examples

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

Step 1

Simplify the expression.

Tap for more steps...

Step 1.1

Move ${(a b^{2} c)}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 1.2

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

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $a b^{2} c$ .

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

Step 2.2

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

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

Step 2.3

Multiply the exponents in ${(b^{2})}^{3}$ .

Tap for more steps...

Step 2.3.1

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

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

Step 2.3.2

Multiply $2$ by $3$ .

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

Step 3

Cancel the common factor of $b^{3}$ and $b^{6}$ .

Tap for more steps...

Step 3.1

Multiply by $1$ .

${(\frac{b^{3} \cdot 1}{a^{3} b^{6} c^{3}})}^{4}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $b^{3}$ out of $a^{3} b^{6} c^{3}$ .

${(\frac{b^{3} \cdot 1}{b^{3} (a^{3} b^{3} c^{3})})}^{4}$

Step 3.2.2

Cancel the common factor.

${(\frac{b^{3} \cdot 1}{b^{3} (a^{3} b^{3} c^{3})})}^{4}$

Step 3.2.3

Rewrite the expression.

${(\frac{1}{a^{3} b^{3} c^{3}})}^{4}$

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 $\frac{1}{a^{3} b^{3} c^{3}}$ .

$\frac{1^{4}}{{(a^{3} b^{3} c^{3})}^{4}}$

Step 4.2

Apply the product rule to $a^{3} b^{3} c^{3}$ .

$\frac{1^{4}}{{(a^{3} b^{3})}^{4} {(c^{3})}^{4}}$

Step 4.3

Apply the product rule to $a^{3} b^{3}$ .

$\frac{1^{4}}{{(a^{3})}^{4} {(b^{3})}^{4} {(c^{3})}^{4}}$

Step 5

One to any power is one.

$\frac{1}{{(a^{3})}^{4} {(b^{3})}^{4} {(c^{3})}^{4}}$

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

Multiply the exponents in ${(a^{3})}^{4}$ .

Tap for more steps...

Step 6.1.1

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

$\frac{1}{a^{3 \cdot 4} {(b^{3})}^{4} {(c^{3})}^{4}}$

Step 6.1.2

Multiply $3$ by $4$ .

$\frac{1}{a^{12} {(b^{3})}^{4} {(c^{3})}^{4}}$

Step 6.2

Multiply the exponents in ${(b^{3})}^{4}$ .

Tap for more steps...

Step 6.2.1

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

$\frac{1}{a^{12} b^{3 \cdot 4} {(c^{3})}^{4}}$

Step 6.2.2

Multiply $3$ by $4$ .

$\frac{1}{a^{12} b^{12} {(c^{3})}^{4}}$

Step 6.3

Multiply the exponents in ${(c^{3})}^{4}$ .

Tap for more steps...

Step 6.3.1

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

$\frac{1}{a^{12} b^{12} c^{3 \cdot 4}}$

Step 6.3.2

Multiply $3$ by $4$ .

$\frac{1}{a^{12} b^{12} c^{12}}$