Algebra Examples

${(- 1)}^{4} \cdot {(- 3)}^{- 3} \cdot 9^{2}$

Step 1

Raise $- 1$ to the power of $4$ .

$1 \cdot {(- 3)}^{- 3} \cdot 9^{2}$

Step 2

Multiply ${(- 3)}^{- 3}$ by $1$ .

${(- 3)}^{- 3} \cdot 9^{2}$

Step 3

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

$\frac{1}{{(- 3)}^{3}} \cdot 9^{2}$

Step 4

Simplify the expression.

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Step 4.1

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

$\frac{1}{- 27} \cdot 9^{2}$

Step 4.2

Move the negative in front of the fraction.

$- \frac{1}{27} \cdot 9^{2}$

Step 4.3

Raise $9$ to the power of $2$ .

$- \frac{1}{27} \cdot 81$

Step 5

Cancel the common factor of $27$ .

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Step 5.1

Move the leading negative in $- \frac{1}{27}$ into the numerator.

$\frac{- 1}{27} \cdot 81$

Step 5.2

Factor $27$ out of $81$ .

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

Step 5.3

Cancel the common factor.

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

Step 5.4

Rewrite the expression.

$- 1 \cdot 3$

Step 6

Multiply $- 1$ by $3$ .

$- 3$