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The problem asks you to simplify and evaluate the expression \( x \cdot x \cdot x \cdot x \) when \( x = -\frac{1}{3} \).

### Step 1: Simplify the expression
The expression \( x \cdot x \cdot x \cdot x \) can be written as \( x^4 \).

### Step 2: Substitute the value of \( x \)
Substitute \( x = -\frac{1}{3} \) into the simplified expression:
\[
x^4 = \left( -\frac{1}{3} \right)^4
\]

### Step 3: Evaluate \( \left( -\frac{1}{3} \right)^4 \)
When raising a negative number to an even power, the result is positive. So,
\[
\left( -\frac{1}{3} \right)^4 = \frac{1^4}{3^4} = \frac{1}{81}
\]

Thus, the value of the expression is \( \frac{1}{81} \).

Let me know if you'd like more details on any step.

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Here are 5 related questions to deepen your understanding:
1. What would happen if the exponent was odd, e.g., \( x^3 \)?
2. How do you simplify an expression like \( x^5 \cdot x^2 \)?
3. How does the sign of the base affect the power when it's raised to an odd exponent?
4. What is the result of \( (-2)^4 \) compared to \( (-2)^3 \)?
5. How do you simplify an expression involving both multiplication and addition of powers?

**Tip:** When raising negative numbers to even powers, the result will always be positive, while odd powers will retain the sign of the base.

Sievennä lauseke ja laske lausekkeen arvo, kun x = -1/3. a) x · x · x · x =

Learn how to simplify and evaluate the expression x · x · x · x = x^4 when x = -1/3. This problem covers exponentiation and properties of negative numbers, including step-by-step simplification and evaluation of (-1/3)^4 = 1/81. Suitable for students in Grades 6-8.

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