use a calculator to evaluate the expression. (round your answer to three decimal places.) (7e^2)^(3/2)
use a calculator to evaluate the expression. (round your answer to three decimal places.) (7e^2)^(3/2)
Answer
Answer:
$146.084$
Explanation:
Step1: Calculate $e^2$
We know that the value of the mathematical constant $e\approx2.71828$. So $e^2=(2.71828)^2\approx7.38906$.
Step2: Calculate $7e^2$
$7e^2 = 7\times7.38906=51.72342$.
Step3: Calculate $(7e^2)^{\frac{3}{2}}$
$(7e^2)^{\frac{3}{2}}=\sqrt{(7e^2)^3}=\sqrt{(51.72342)^3}$. First, $(51.72342)^3 = 51.72342\times51.72342\times51.72342\approx13693.377$. Then $\sqrt{13693.377}\approx146.084$.