Question

solve the following equation with a rational exponent: 2x{3/2}+=16
A.no solution B.8 C.3 D.84

Answer 1

solve the following equation with a rational exponent: 5x{4/3}=80

Answer 2

To solve the equation \( 2x^{3/2} = 16 \), follow these steps:

1. Divide both sides by 2:

\[
x^{3/2} = \frac{16}{2} = 8
\]

2. Now, to eliminate the rational exponent, raise both sides to the power of \( \frac{2}{3} \):

\[
x = 8^{2/3}
\]

3. Calculate \( 8^{2/3} \). First, we can find the cube root of 8, which is 2:

\[
8^{1/3} = 2
\]

4. Then square it:

\[
(8^{1/3})^2 = 2^2 = 4
\]

Thus, we find:

\[
x = 4
\]

Now let's check the options provided (A: no solution, B: 8, C: 3, D: 84). Since \( x = 4 \) is not listed among the options, there seems to be a discrepancy.

To summarize, the solution to the equation \( 2x^{3/2} = 16 \) is \( x = 4 \), but since this value is not in the given choices, the answer would lean towards option A: no solution from the given choices.

Answer 3

To solve the equation \( 5x^{4/3} = 80 \), follow these steps:

1. **Divide both sides by 5**:
\[
x^{4/3} = \frac{80}{5} = 16
\]

2. **Raise both sides to the power of \( \frac{3}{4} \)** to eliminate the rational exponent:
\[
x = 16^{3/4}
\]

3. **Calculate \( 16^{3/4} \)**:
- First, find the fourth root of 16:
\[
16^{1/4} = 2
\]
- Then, raise that result to the power of 3:
\[
(16^{1/4})^3 = 2^3 = 8
\]

Thus, the solution is:
\[
x = 8
\]

So, the value of \( x \) is \( 8 \).