Which expression is equivalent to 3, to the power 0 , dot, 3, to the power minus 3 , question mark30⋅3−3?

To evaluate the expression \( 3^0 \cdot 3^{-3} \), we can use the laws of exponents.

### Step 1: Evaluate \( 3^0 \)
Any number raised to the power of 0 is 1:
\[
3^0 = 1
\]

### Step 2: Evaluate \( 3^{-3} \)
A negative exponent indicates the reciprocal:
\[
3^{-3} = \frac{1}{3^3} = \frac{1}{27}
\]

### Step 3: Multiply the results
Now, multiply the results from Step 1 and Step 2:
\[
1 \cdot \frac{1}{27} = \frac{1}{27}
\]

So, the expression \( 3^0 \cdot 3^{-3} \) is equivalent to \(\frac{1}{27}\).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the value of \( 2^0 \cdot 2^{-2} \)?
2. How does the expression change if you replace \(3^{-3}\) with \(3^3\)?
3. What is the value of \( 5^0 \cdot 5^{-4} \)?
4. Simplify the expression \( x^0 \cdot x^{-1} \) for any non-zero \(x\).
5. What is the value of \( 4^{-2} \cdot 4^2 \)?

**Tip:** Remember that any non-zero number raised to the power of 0 equals 1.

Learn how to evaluate the expression 3 raised to the power of 0 multiplied by 3 raised to the power of -3 using the laws of exponents. Understand why any number raised to the power of 0 equals 1 and how negative exponents indicate reciprocals. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation