Algebra Examples

${(1 - 3 \cdot {(\frac{3^{4}}{4})}^{- 1} \cdot \frac{3^{3}}{4})}^{10}$

Step 1

Simplify each term.

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Step 1.1

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

${(1 - 3 \cdot {(\frac{3^{4}}{4})}^{- 1} \cdot \frac{27}{4})}^{10}$

Step 1.2

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

${(1 - 3 \cdot {(\frac{81}{4})}^{- 1} \cdot \frac{27}{4})}^{10}$

Step 1.3

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

${(1 - 3 \cdot \frac{4}{81} \cdot \frac{27}{4})}^{10}$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $- 3$ .

${(1 + 3 (- 1) \cdot \frac{4}{81} \cdot \frac{27}{4})}^{10}$

Step 1.4.2

Factor $3$ out of $81$ .

${(1 + 3 \cdot - 1 \cdot \frac{4}{3 \cdot 27} \cdot \frac{27}{4})}^{10}$

Step 1.4.3

Cancel the common factor.

${(1 + 3 \cdot - 1 \cdot \frac{4}{3 \cdot 27} \cdot \frac{27}{4})}^{10}$

Step 1.4.4

Rewrite the expression.

${(1 - 1 \cdot \frac{4}{27} \cdot \frac{27}{4})}^{10}$

Step 1.5

Rewrite $- 1 (\frac{4}{27})$ as $- (\frac{4}{27})$ .

${(1 - (\frac{4}{27}) \cdot \frac{27}{4})}^{10}$

Step 1.6

Cancel the common factor of $4$ .

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Step 1.6.1

Move the leading negative in $- (\frac{4}{27})$ into the numerator.

${(1 + \frac{- 4}{27} \cdot \frac{27}{4})}^{10}$

Step 1.6.2

Factor $4$ out of $- 4$ .

${(1 + \frac{4 (- 1)}{27} \cdot \frac{27}{4})}^{10}$

Step 1.6.3

Cancel the common factor.

${(1 + \frac{4 \cdot - 1}{27} \cdot \frac{27}{4})}^{10}$

Step 1.6.4

Rewrite the expression.

${(1 + \frac{- 1}{27} \cdot 27)}^{10}$

Step 1.7

Cancel the common factor of $27$ .

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Step 1.7.1

Cancel the common factor.

${(1 + \frac{- 1}{27} \cdot 27)}^{10}$

Step 1.7.2

Rewrite the expression.

${(1 - 1)}^{10}$

Step 2

Simplify the expression.

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Step 2.1

Subtract $1$ from $1$ .

$0^{10}$

Step 2.2

Raising $0$ to any positive power yields $0$ .

$0$