To solve the equation \( 5x^{4/3} = 80 \), we can follow these steps:
-
Divide both sides by 5: \[ x^{4/3} = \frac{80}{5} = 16 \]
-
To eliminate the rational exponent, raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \): \[ x = 16^{3/4} \]
-
Calculate \( 16^{3/4} \):
-
First, find \( 16^{1/4} \): \[ 16^{1/4} = 2 \quad (\text{since } 2^4 = 16) \]
-
Next, raise \( 2 \) to the power of 3: \[ 2^3 = 8 \]
-
-
Therefore, \[ x = 8 \]
So, the solution to the equation \( 5x^{4/3} = 80 \) is:
8
1 answer