Evaluate Using the Given Value f(40)=1000(0.5)^(40/30)

$f (40) = 1000 {(0.5)}^{\frac{40}{30}}$

Step 1

Cancel the common factor of $40$ and $30$ .

Factor $10$ out of $40$ .

$f (40) = 1000 \cdot {0.5}^{\frac{10 (4)}{30}}$

Cancel the common factors.

Factor $10$ out of $30$ .

$f (40) = 1000 \cdot {0.5}^{\frac{10 \cdot 4}{10 \cdot 3}}$

Cancel the common factor.

$f (40) = 1000 \cdot {0.5}^{\frac{10 \cdot 4}{10 \cdot 3}}$

Rewrite the expression.

$f (40) = 1000 \cdot {0.5}^{\frac{4}{3}}$

Step 2

Simplify the expression.

Raise $0.5$ to the power of $\frac{4}{3}$ .

$f (40) = 1000 \cdot 0.39685026$

Multiply $1000$ by $0.39685026$ .

$f (40) = 396.85026299$