Linear Algebra Examples

$((7 - 12) (9^{- 9})) - 5$

Step 1

Simplify each term.

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Step 1.1

Subtract $12$ from $7$ .

$- 5 \cdot 9^{- 9} - 5$

Step 1.2

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

$- 5 \cdot \frac{1}{9^{9}} - 5$

Step 1.3

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

$- 5 \cdot \frac{1}{387420489} - 5$

Step 1.4

Combine $- 5$ and $\frac{1}{387420489}$ .

$\frac{- 5}{387420489} - 5$

Step 1.5

Move the negative in front of the fraction.

$- \frac{5}{387420489} - 5$

Step 2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{387420489}{387420489}$ .

$- \frac{5}{387420489} - 5 \cdot \frac{387420489}{387420489}$

Step 3

Combine $- 5$ and $\frac{387420489}{387420489}$ .

$- \frac{5}{387420489} + \frac{- 5 \cdot 387420489}{387420489}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 5 - 5 \cdot 387420489}{387420489}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 5$ by $387420489$ .

$\frac{- 5 - 1937102445}{387420489}$

Step 5.2

Subtract $1937102445$ from $- 5$ .

$\frac{- 1937102450}{387420489}$

Step 6

Move the negative in front of the fraction.

$- \frac{1937102450}{387420489}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1937102450}{387420489}$

Decimal Form:

$- 5.00000001 \dots$

Mixed Number Form:

$- 5 \frac{5}{387420489}$