Algebra Examples

$2^{- 2} \cdot (12 \cdot 3) - 5^{3}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1}{2^{2}} \cdot (12 \cdot 3) - 5^{3}$

Step 1.2

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

$\frac{1}{4} \cdot (12 \cdot 3) - 5^{3}$

Step 1.3

Multiply $12$ by $3$ .

$\frac{1}{4} \cdot 36 - 5^{3}$

Step 1.4

Cancel the common factor of $4$ .

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Step 1.4.1

Factor $4$ out of $36$ .

$\frac{1}{4} \cdot (4 (9)) - 5^{3}$

Step 1.4.2

Cancel the common factor.

$\frac{1}{4} \cdot (4 \cdot 9) - 5^{3}$

Step 1.4.3

Rewrite the expression.

$9 - 5^{3}$

Step 1.5

Raise $5$ to the power of $3$ .

$9 - 1 \cdot 125$

Step 1.6

Multiply $- 1$ by $125$ .

$9 - 125$

Step 2

Subtract $125$ from $9$ .

$- 116$