Evaluate Using the Given Value f(70)=1000(0.5)^(70/30)

$f (70) = 1000 {(0.5)}^{\frac{70}{30}}$

Step 1

Cancel the common factor of $70$ and $30$ .

Factor $10$ out of $70$ .

$f (70) = 1000 \cdot {0.5}^{\frac{10 (7)}{30}}$

Cancel the common factors.

Factor $10$ out of $30$ .

$f (70) = 1000 \cdot {0.5}^{\frac{10 \cdot 7}{10 \cdot 3}}$

Cancel the common factor.

$f (70) = 1000 \cdot {0.5}^{\frac{10 \cdot 7}{10 \cdot 3}}$

Rewrite the expression.

$f (70) = 1000 \cdot {0.5}^{\frac{7}{3}}$

Step 2

Simplify the expression.

Raise $0.5$ to the power of $\frac{7}{3}$ .

$f (70) = 1000 \cdot 0.19842513$

Multiply $1000$ by $0.19842513$ .

$f (70) = 198.42513149$