Algebra Examples

${(\frac{4^{0} c^{2} d^{3} f}{2 c^{- 4} d^{- 5}})}^{- 3}$

Step 1

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

${(\frac{4^{0} c^{2} d^{3} f c^{4}}{2 d^{- 5}})}^{- 3}$

Step 2

Move $d^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{4^{0} c^{2} d^{3} f c^{4} d^{5}}{2})}^{- 3}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Move $c^{4}$ .

${(\frac{4^{0} (c^{4} c^{2}) d^{3} f d^{5}}{2})}^{- 3}$

Step 3.1.2

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

${(\frac{4^{0} c^{4 + 2} d^{3} f d^{5}}{2})}^{- 3}$

Step 3.1.3

Add $4$ and $2$ .

${(\frac{4^{0} c^{6} d^{3} f d^{5}}{2})}^{- 3}$

Step 3.2

Simplify $4^{0} c^{6} d^{3} f$ .

${(\frac{c^{6} d^{3} f d^{5}}{2})}^{- 3}$

Step 3.3

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

Tap for more steps...

Step 3.3.1

Move $d^{5}$ .

${(\frac{c^{6} (d^{5} d^{3}) f}{2})}^{- 3}$

Step 3.3.2

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

${(\frac{c^{6} d^{5 + 3} f}{2})}^{- 3}$

Step 3.3.3

Add $5$ and $3$ .

${(\frac{c^{6} d^{8} f}{2})}^{- 3}$

Step 4

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

${(\frac{2}{c^{6} d^{8} f})}^{3}$

Step 5

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

Tap for more steps...

Step 5.1

Apply the product rule to $\frac{2}{c^{6} d^{8} f}$ .

$\frac{2^{3}}{{(c^{6} d^{8} f)}^{3}}$

Step 5.2

Apply the product rule to $c^{6} d^{8} f$ .

$\frac{2^{3}}{{(c^{6} d^{8})}^{3} f^{3}}$

Step 5.3

Apply the product rule to $c^{6} d^{8}$ .

$\frac{2^{3}}{{(c^{6})}^{3} {(d^{8})}^{3} f^{3}}$

Step 6

Raise $2$ to the power of $3$ .

$\frac{8}{{(c^{6})}^{3} {(d^{8})}^{3} f^{3}}$

Step 7

Simplify the denominator.

Tap for more steps...

Step 7.1

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

Tap for more steps...

Step 7.1.1

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

$\frac{8}{c^{6 \cdot 3} {(d^{8})}^{3} f^{3}}$

Step 7.1.2

Multiply $6$ by $3$ .

$\frac{8}{c^{18} {(d^{8})}^{3} f^{3}}$

Step 7.2

Multiply the exponents in ${(d^{8})}^{3}$ .

Tap for more steps...

Step 7.2.1

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

$\frac{8}{c^{18} d^{8 \cdot 3} f^{3}}$

Step 7.2.2

Multiply $8$ by $3$ .

$\frac{8}{c^{18} d^{24} f^{3}}$