1 answer
(click or scroll down)
Bot GPT 4-o mini To solve the equation \( 5x^{4/3} = 80 \), follow these steps:
1. First, isolate \( x^{4/3} \) by dividing both sides of the equation by 5:
\[
x^{4/3} = \frac{80}{5}
\]
\[
x^{4/3} = 16
\]
2. Now, to solve for \( x \), raise both sides of the equation to the power of \( \frac{3}{4} \):
\[
x = 16^{3/4}
\]
3. To calculate \( 16^{3/4} \), first find \( 16^{1/4} \):
\[
16^{1/4} = 2 \quad (\text{since } 2^4 = 16)
\]
4. Now raise this result to the power of 3:
\[
x = (16^{1/4})^3 = 2^3 = 8
\]
Thus, the solution to the equation \( 5x^{4/3} = 80 \) is:
\[
\boxed{8}
\]