Algebra Examples

${(\frac{- 2 d^{11} f^{5}}{4 d^{- 2} f^{2}})}^{2}$

Step 1

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

${(\frac{- 2 d^{11} f^{5} d^{2}}{4 f^{2}})}^{2}$

Step 2

Multiply $d^{11}$ by $d^{2}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $d^{2}$ .

${(\frac{- 2 (d^{2} d^{11}) f^{5}}{4 f^{2}})}^{2}$

Step 2.2

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

${(\frac{- 2 d^{2 + 11} f^{5}}{4 f^{2}})}^{2}$

Step 2.3

Add $2$ and $11$ .

${(\frac{- 2 d^{13} f^{5}}{4 f^{2}})}^{2}$

Step 3

Cancel the common factor of $- 2$ and $4$ .

Tap for more steps...

Step 3.1

Factor $2$ out of $- 2 d^{13} f^{5}$ .

${(\frac{2 (- d^{13} f^{5})}{4 f^{2}})}^{2}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $2$ out of $4 f^{2}$ .

${(\frac{2 (- d^{13} f^{5})}{2 (2 f^{2})})}^{2}$

Step 3.2.2

Cancel the common factor.

${(\frac{2 (- d^{13} f^{5})}{2 (2 f^{2})})}^{2}$

Step 3.2.3

Rewrite the expression.

${(\frac{- d^{13} f^{5}}{2 f^{2}})}^{2}$

Step 4

Cancel the common factor of $f^{5}$ and $f^{2}$ .

Tap for more steps...

Step 4.1

Factor $f^{2}$ out of $- d^{13} f^{5}$ .

${(\frac{f^{2} (- d^{13} f^{3})}{2 f^{2}})}^{2}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $f^{2}$ out of $2 f^{2}$ .

${(\frac{f^{2} (- d^{13} f^{3})}{f^{2} \cdot 2})}^{2}$

Step 4.2.2

Cancel the common factor.

${(\frac{f^{2} (- d^{13} f^{3})}{f^{2} \cdot 2})}^{2}$

Step 4.2.3

Rewrite the expression.

${(\frac{- d^{13} f^{3}}{2})}^{2}$

Step 5

Move the negative in front of the fraction.

${(- \frac{d^{13} f^{3}}{2})}^{2}$

Step 6

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

Tap for more steps...

Step 6.1

Apply the product rule to $- \frac{d^{13} f^{3}}{2}$ .

${(- 1)}^{2} {(\frac{d^{13} f^{3}}{2})}^{2}$

Step 6.2

Apply the product rule to $\frac{d^{13} f^{3}}{2}$ .

${(- 1)}^{2} \frac{{(d^{13} f^{3})}^{2}}{2^{2}}$

Step 6.3

Apply the product rule to $d^{13} f^{3}$ .

${(- 1)}^{2} \frac{{(d^{13})}^{2} {(f^{3})}^{2}}{2^{2}}$

Step 7

Simplify the expression.

Tap for more steps...

Step 7.1

Raise $- 1$ to the power of $2$ .

$1 \frac{{(d^{13})}^{2} {(f^{3})}^{2}}{2^{2}}$

Step 7.2

Multiply $\frac{{(d^{13})}^{2} {(f^{3})}^{2}}{2^{2}}$ by $1$ .

$\frac{{(d^{13})}^{2} {(f^{3})}^{2}}{2^{2}}$

Step 8

Simplify the numerator.

Tap for more steps...

Step 8.1

Multiply the exponents in ${(d^{13})}^{2}$ .

Tap for more steps...

Step 8.1.1

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

$\frac{d^{13 \cdot 2} {(f^{3})}^{2}}{2^{2}}$

Step 8.1.2

Multiply $13$ by $2$ .

$\frac{d^{26} {(f^{3})}^{2}}{2^{2}}$

Step 8.2

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

Tap for more steps...

Step 8.2.1

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

$\frac{d^{26} f^{3 \cdot 2}}{2^{2}}$

Step 8.2.2

Multiply $3$ by $2$ .

$\frac{d^{26} f^{6}}{2^{2}}$

Step 9

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

$\frac{d^{26} f^{6}}{4}$