Algebra Examples

$2^{- 4} - 3^{3} \cdot 5^{- 2}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1}{2^{4}} - 3^{3} \cdot 5^{- 2}$

Step 1.2

Raise $2$ to the power of $4$ .

$\frac{1}{16} - 3^{3} \cdot 5^{- 2}$

Step 1.3

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

$\frac{1}{16} - 1 \cdot 27 \cdot 5^{- 2}$

Step 1.4

Multiply $- 1$ by $27$ .

$\frac{1}{16} - 27 \cdot 5^{- 2}$

Step 1.5

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

$\frac{1}{16} - 27 \cdot \frac{1}{5^{2}}$

Step 1.6

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

$\frac{1}{16} - 27 \cdot \frac{1}{25}$

Step 1.7

Combine $- 27$ and $\frac{1}{25}$ .

$\frac{1}{16} + \frac{- 27}{25}$

Step 1.8

Move the negative in front of the fraction.

$\frac{1}{16} - \frac{27}{25}$

Step 2

To write $\frac{1}{16}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{1}{16} \cdot \frac{25}{25} - \frac{27}{25}$

Step 3

To write $- \frac{27}{25}$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{1}{16} \cdot \frac{25}{25} - \frac{27}{25} \cdot \frac{16}{16}$

Step 4

Write each expression with a common denominator of $400$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{16}$ by $\frac{25}{25}$ .

$\frac{25}{16 \cdot 25} - \frac{27}{25} \cdot \frac{16}{16}$

Step 4.2

Multiply $16$ by $25$ .

$\frac{25}{400} - \frac{27}{25} \cdot \frac{16}{16}$

Step 4.3

Multiply $\frac{27}{25}$ by $\frac{16}{16}$ .

$\frac{25}{400} - \frac{27 \cdot 16}{25 \cdot 16}$

Step 4.4

Multiply $25$ by $16$ .

$\frac{25}{400} - \frac{27 \cdot 16}{400}$

Step 5

Combine the numerators over the common denominator.

$\frac{25 - 27 \cdot 16}{400}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 27$ by $16$ .

$\frac{25 - 432}{400}$

Step 6.2

Subtract $432$ from $25$ .

$\frac{- 407}{400}$

Step 7

Move the negative in front of the fraction.

$- \frac{407}{400}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{407}{400}$

Decimal Form:

$- 1.0175$

Mixed Number Form:

$- 1 \frac{7}{400}$