Question

I'm studying for my math exam and struggling with exponents. Can you find an explanation for how to condense and compute an expression like 3×3×3×3×3 using exponents? Provide the step-by-step calculation for the solution.

Answer 1

Of course! To condense and compute an expression like \( 3 \times 3 \times 3 \times 3 \times 3 \) using exponents, you can follow these steps:

### Step 1: Identify the Base and the Number of Times it is Multiplied
In the expression \( 3 \times 3 \times 3 \times 3 \times 3 \), the base is \( 3 \), and it is multiplied together \( 5 \) times.

### Step 2: Write the Expression Using Exponents
You can express this repeated multiplication using exponents. The exponent indicates how many times the base is multiplied by itself. In this case, we can write:
\[
3 \times 3 \times 3 \times 3 \times 3 = 3^5
\]

### Step 3: Compute the Value
Now, let's calculate the value of \( 3^5 \):
\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3
\]

To compute \( 3^5 \), you can perform the multiplications step-by-step:

1. First, multiply the first two \( 3 \)'s:
\[
3 \times 3 = 9
\]

2. Now multiply the result by the next \( 3 \):
\[
9 \times 3 = 27
\]

3. Then, multiply that result by the next \( 3 \):
\[
27 \times 3 = 81
\]

4. Finally, multiply by the last \( 3 \):
\[
81 \times 3 = 243
\]

### Final Answer
Thus, the value of \( 3^5 \) is:
\[
3^5 = 243
\]

So, \( 3 \times 3 \times 3 \times 3 \times 3 \) condensed and computed using exponents is \( 3^5 = 243 \).