Question
Solve the following occasion with a rational exponent 5x 4/3 = 80 12 16 8 40.32
Answers
GPT-4o mini
To solve the equation \( 5x^{4/3} = 80 \), start by isolating \( x^{4/3} \).
1. Divide both sides by 5:
\[
x^{4/3} = \frac{80}{5} = 16
\]
2. To eliminate the rational exponent, raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):
\[
x = 16^{3/4}
\]
3. Calculate \( 16^{3/4} \):
We know that \( 16 = 2^4 \).
\[
x = (2^4)^{3/4} = 2^{4 \cdot \frac{3}{4}} = 2^3 = 8
\]
Thus, the solution is:
\[
\boxed{8}
\]
1. Divide both sides by 5:
\[
x^{4/3} = \frac{80}{5} = 16
\]
2. To eliminate the rational exponent, raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):
\[
x = 16^{3/4}
\]
3. Calculate \( 16^{3/4} \):
We know that \( 16 = 2^4 \).
\[
x = (2^4)^{3/4} = 2^{4 \cdot \frac{3}{4}} = 2^3 = 8
\]
Thus, the solution is:
\[
\boxed{8}
\]