Evaluate (cube root of 17 + 10 pi) divided by (e^5 + 90).

Step-by-step solution

1. 1

   Read the grouping before computing anything. "All divided by" means the entire sum $\sqrt[3]{17}+10\pi$ sits over the entire sum $e^5+90$. Written flat it would be $(\sqrt[3]{17}+10\pi)/(e^5+90)$ - the brackets are not optional, and dropping them is the main hazard in this problem.

2. 2

   Evaluate the numerator's two pieces. Carry more digits than the final answer needs:

   $\sqrt[3]{17}=2.57128,\qquad 10\pi=31.41593$

   (A quick sanity check on the cube root: $2.5^3=15.6$ and $2.6^3=17.6$, so $\sqrt[3]{17}$ must lie between $2.5$ and $2.6$ ✓.)

3. 3

   Add to get the numerator.

   $2.57128+31.41593=33.98721$

4. 4

   Evaluate the denominator. With $e=2.718282$,

   $e^{5}=148.41316\quad\Longrightarrow\quad e^{5}+90=238.41316$

5. 5

   Divide.

   $\frac{33.98721}{238.41316}=0.1425559$

6. 6

   Estimate independently to confirm. Rounding crudely, $\tfrac{34}{238}\approx0.1429$ - within $0.0004$ of the computed value, which confirms no decimal-point or grouping error. To four decimal places the answer is $0.1426$.