Precalculus Examples

$a (10) = 100 {(3)}^{- 0.5 \cdot 10}$

Step 1

Simplify.

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Step 1.1

Multiply $- 0.5$ by $10$ .

$a (10) = 100 \cdot 3^{- 5}$

Step 1.2

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

$a (10) = 100 \cdot \frac{1}{3^{5}}$

Step 1.3

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

$a (10) = 100 \cdot \frac{1}{243}$

Step 1.4

Divide $1$ by $243$ .

$a (10) = 100 \cdot 0.00411522$

Step 1.5

Multiply $100$ by $0.00411522$ .

$a (10) = 0.41152263$

Step 2

Divide each term in $a (10) = 0.41152263$ by $10$ and simplify.

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Step 2.1

Divide each term in $a (10) = 0.41152263$ by $10$ .

$\frac{a (10)}{10} = \frac{0.41152263}{10}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $10$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{a \cdot 10}{10} = \frac{0.41152263}{10}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{0.41152263}{10}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0.41152263$ by $10$ .

$a = 0.04115226$