Algebra Examples

${(3^{8} \cdot 2^{- 5} \cdot 9^{0})}^{- 2} \cdot {(\frac{2^{- 2}}{3^{3}})}^{4} \cdot 3^{28}$

Step 1

Raise $3$ to the power of $8$ .

${(6561 \cdot 2^{- 5} \cdot 9^{0})}^{- 2} \cdot {(\frac{2^{- 2}}{3^{3}})}^{4} \cdot 3^{28}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(6561 \cdot \frac{1}{2^{5}} \cdot 9^{0})}^{- 2} \cdot {(\frac{2^{- 2}}{3^{3}})}^{4} \cdot 3^{28}$

Step 3

Raise $2$ to the power of $5$ .

${(6561 \cdot \frac{1}{32} \cdot 9^{0})}^{- 2} \cdot {(\frac{2^{- 2}}{3^{3}})}^{4} \cdot 3^{28}$

Step 4

Combine $6561$ and $\frac{1}{32}$ .

${(\frac{6561}{32} \cdot 9^{0})}^{- 2} \cdot {(\frac{2^{- 2}}{3^{3}})}^{4} \cdot 3^{28}$

Step 5

Anything raised to $0$ is $1$ .

${(\frac{6561}{32} \cdot 1)}^{- 2} \cdot {(\frac{2^{- 2}}{3^{3}})}^{4} \cdot 3^{28}$

Step 6

Multiply $\frac{6561}{32}$ by $1$ .

${(\frac{6561}{32})}^{- 2} \cdot {(\frac{2^{- 2}}{3^{3}})}^{4} \cdot 3^{28}$

Step 7

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

${(\frac{32}{6561})}^{2} \cdot {(\frac{2^{- 2}}{3^{3}})}^{4} \cdot 3^{28}$

Step 8

Apply the product rule to $\frac{32}{6561}$ .

$\frac{32^{2}}{6561^{2}} \cdot {(\frac{2^{- 2}}{3^{3}})}^{4} \cdot 3^{28}$

Step 9

Raise $32$ to the power of $2$ .

$\frac{1024}{6561^{2}} \cdot {(\frac{2^{- 2}}{3^{3}})}^{4} \cdot 3^{28}$

Step 10

Raise $6561$ to the power of $2$ .

$\frac{1024}{43046721} \cdot {(\frac{2^{- 2}}{3^{3}})}^{4} \cdot 3^{28}$

Step 11

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

$\frac{1024}{43046721} \cdot {(\frac{1}{3^{3} \cdot 2^{2}})}^{4} \cdot 3^{28}$

Step 12

Simplify the denominator.

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Step 12.1

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

$\frac{1024}{43046721} \cdot {(\frac{1}{27 \cdot 2^{2}})}^{4} \cdot 3^{28}$

Step 12.2

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

$\frac{1024}{43046721} \cdot {(\frac{1}{27 \cdot 4})}^{4} \cdot 3^{28}$

Step 13

Multiply $27$ by $4$ .

$\frac{1024}{43046721} \cdot {(\frac{1}{108})}^{4} \cdot 3^{28}$

Step 14

Apply the product rule to $\frac{1}{108}$ .

$\frac{1024}{43046721} \cdot \frac{1^{4}}{108^{4}} \cdot 3^{28}$

Step 15

Combine.

$\frac{1024 \cdot 1^{4}}{43046721 \cdot 108^{4}} \cdot 3^{28}$

Step 16

One to any power is one.

$\frac{1024 \cdot 1}{43046721 \cdot 108^{4}} \cdot 3^{28}$

Step 17

Raise $108$ to the power of $4$ .

$\frac{1024 \cdot 1}{43046721 \cdot 136048896} \cdot 3^{28}$

Step 18

Multiply $1024$ by $1$ .

$\frac{1024}{43046721 \cdot 136048896} \cdot 3^{28}$

Step 19

Multiply $43046721$ by $136048896$ .

$\frac{1024}{5856458868470016} \cdot 3^{28}$

Step 20

Cancel the common factor of $1024$ and $5856458868470016$ .

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Step 20.1

Factor $256$ out of $1024$ .

$\frac{256 (4)}{5856458868470016} \cdot 3^{28}$

Step 20.2

Cancel the common factors.

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Step 20.2.1

Factor $256$ out of $5856458868470016$ .

$\frac{256 \cdot 4}{256 \cdot 22876792454961} \cdot 3^{28}$

Step 20.2.2

Cancel the common factor.

$\frac{256 \cdot 4}{256 \cdot 22876792454961} \cdot 3^{28}$

Step 20.2.3

Rewrite the expression.

$\frac{4}{22876792454961} \cdot 3^{28}$

Step 21

Raise $3$ to the power of $28$ .

$\frac{4}{22876792454961} \cdot 22876792454961$

Step 22

Cancel the common factor of $22876792454961$ .

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Step 22.1

Cancel the common factor.

$\frac{4}{22876792454961} \cdot 22876792454961$

Step 22.2

Rewrite the expression.

$4$