Solve for x

Question

x^10/3=27 times x^1/3

Answer 1

To solve the equation

$$x^{10/3}=27\cdot x^{1/3},$$

we start by rewriting $27$ as $3^3$:

$$x^{10/3}=3^3\cdot x^{1/3}.$$

Now, we can rearrange the equation:

$$x^{10/3}-3^3\cdot x^{1/3}=0.$$

Next, we can factor out $x^{1/3}$:

$$x^{1/3}(x^{10/3-1/3}-27)=0.$$

This simplifies to:

$$x^{1/3}(x^3-27)=0.$$

Now, we have two factors that can be set to zero:

1. $x^{1/3}=0$
2. $x^3-27=0$

From the first factor, $x^{1/3}=0$ gives:

$$x=0.$$

From the second factor, $x^3-27=0$ gives:

$$x^3=27⟹x={27}^{1/3}=3.$$

Thus, the solutions for $x$ are:

$$\boxed{{\displaystyle 0}}\text{ and }\boxed{{\displaystyle 3}}.$$

Answer 2

Theres not mutiple solutions
27^11/3
1/3
3
9

Answer 3

Let's go through the equation step-by-step and clarify the solutions.

Given the equation:

$$x^{10/3}=27\cdot x^{1/3}$$

Step 1: Rewrite the equation

First, note that $27=3^3$. We can rewrite the equation as:

$$x^{10/3}=3^3\cdot x^{1/3}$$

Step 2: Move all terms to one side

Rearranging gives:

$$x^{10/3}-3^3\cdot x^{1/3}=0$$

Step 3: Factor out common terms

Factor out $x^{1/3}$:

$$x^{1/3}(x^{10/3-1/3}-27)=0$$

This simplifies to:

$$x^{1/3}(x^3-27)=0$$

Step 4: Set each factor to zero

This gives us two cases:

1. $x^{1/3}=0$ which results in $x=0$.
2. $x^3-27=0$ which leads to $x^3=27$. Solving this gives:

$$x={27}^{1/3}=3.$$

Final Solutions

Thus, the solutions are $x=0$ and $x=3$.

Clarification of Misunderstanding

If you're looking for specific values such as ${27}^{11/3}$, $1/3$, $3$, or $9$, it seems there may be some confusion.

From solving the equation:

• $x=3$ is valid.
• The other value $x=0$ is also a solution.

If you're looking for specific values to check against possible solutions or confirming calculations, please clarify further. The valid solutions for the given equation are:

$$\boxed{{\displaystyle 0}}\text{ and }\boxed{{\displaystyle 3}}.$$