Question

Question
Solve Start Fraction x over 18 End Fraction equals Start Fraction 72 over x cubed End Fraction semi-colon x not equals 0.
(1 point)
Responses

plus or minus 6
Image with alt text: plus or minus 6

plus or minus 36
Image with alt text: plus or minus 36

plus or minus 4
Image with alt text: plus or minus 4

plus or minus 2

Answer 1

To solve the equation

\[
\frac{x}{18} = \frac{72}{x^3}
\]

we can start by cross-multiplying to eliminate the fractions:

\[
x \cdot x^3 = 72 \cdot 18
\]

This simplifies to:

\[
x^4 = 1296
\]

Next, we take the fourth root of both sides:

\[
x = \pm \sqrt[4]{1296}
\]

Now, we need to find \(\sqrt[4]{1296}\). First, find the prime factorization of 1296:

\[
1296 = 36 \times 36 = 6^2 \times 6^2 = (6^2)^2 = 6^4
\]

So,

\[
1296 = 6^4
\]

Therefore,

\[
\sqrt[4]{1296} = 6
\]

Thus, we get:

\[
x = \pm 6
\]

The final answer is:

\[
\boxed{\pm 6}
\]