Questions: Solve for (x) [ (x+7)^5 / 3=32 x= ]

Transcript text: Solve for $x$ \[ \begin{array}{l} (x+7)^{5 / 3}=32 \\ x= \end{array} \]

Solution

Solution Steps

To solve for $ x $ in the equation $(x+7)^{5/3} = 32$, we can follow these steps:

Isolate the term with the exponent by taking both sides of the equation to the power of $ \frac{3}{5} $.
Subtract 7 from both sides to solve for $ x $.

Step 1: Isolate the Term with the Exponent

Given the equation: \[ (x + 7)^{5/3} = 32 \] To isolate $ x + 7 $, we take both sides of the equation to the power of $ \frac{3}{5} $: \[ (x + 7) = 32^{3/5} \]

Step 2: Calculate the Right-Hand Side

Calculate $ 32^{3/5} $: \[ 32^{3/5} \approx 8 \]

Step 3: Solve for $ x $

Subtract 7 from both sides to solve for $ x $: \[ x = 32^{3/5} - 7 \] \[ x \approx 8 - 7 \] \[ x \approx 1 \]