Precalculus Examples

$y = 100 {(0.5)}^{\frac{10}{4}}$

Step 1

Remove parentheses.

$y = 100 \cdot {0.5}^{\frac{10}{4}}$

Step 2

Simplify $100 \cdot {0.5}^{\frac{10}{4}}$ .

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Step 2.1

Cancel the common factor of $10$ and $4$ .

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Step 2.1.1

Factor $2$ out of $10$ .

$y = 100 \cdot {0.5}^{\frac{2 (5)}{4}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $4$ .

$y = 100 \cdot {0.5}^{\frac{2 \cdot 5}{2 \cdot 2}}$

Step 2.1.2.2

Cancel the common factor.

$y = 100 \cdot {0.5}^{\frac{2 \cdot 5}{2 \cdot 2}}$

Step 2.1.2.3

Rewrite the expression.

$y = 100 \cdot {0.5}^{\frac{5}{2}}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Rewrite $0.5$ as ${0.70710678}^{2}$ .

$y = 100 \cdot {({0.70710678}^{2})}^{\frac{5}{2}}$

Step 2.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y = 100 \cdot {0.70710678}^{2 (\frac{5}{2})}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

$y = 100 \cdot {0.70710678}^{2 (\frac{5}{2})}$

Step 2.3.2

Rewrite the expression.

$y = 100 \cdot {0.70710678}^{5}$

Step 2.4

Simplify the expression.

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Step 2.4.1

Raise $0.70710678$ to the power of $5$ .

$y = 100 \cdot 0.17677669$

Step 2.4.2

Multiply $100$ by $0.17677669$ .

$y = 17.67766952$