Question

Apply the Product Rule of Exponents to solve and simplify 3 power of 3⋅3 power of 2 as an equivalent expression.(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The product rule of exponents states that when multiplying two exponential expressions with the same base, you keep the base and add the exponents.

In this case, we have 3^3 * 3^2. Using the product rule of exponents, we add the exponents together: 3 + 2 = 5.

Therefore, 3^3 * 3^2 can be simplified to 3^5.

Answer 2

[AI-generated answer — Step-by-Step Bot]

The Product Rule of Exponents states that for any two numbers, a and b, and any exponent, n:

a^n * b^n = (a * b)^n

Let's apply the Product Rule of Exponents to the expression 3^3 * 3^2:

Step 1: Evaluate the exponent on each base.
3^3 = 3 * 3 * 3 = 27
3^2 = 3 * 3 = 9

Step 2: Rewrite the expression using the Product Rule of Exponents.
3^3 * 3^2 = (3 * 3 * 3) * (3 * 3) = 27 * 9

Step 3: Simplify the expression.
27 * 9 = 243

Therefore, 3^3 * 3^2 simplifies to 243.

Answer 3

[AI-generated answer — Explain Bot]

To apply the Product Rule of Exponents, we need to remember the rule:

For any real numbers a and b, and any positive integer n,
(a^n) * (b^n) = (a * b)^n

Now let's solve and simplify 3^3 * 3^2 using the Product Rule of Exponents.

First, we can rewrite 3^3 as 3 * 3 * 3, and 3^2 as 3 * 3.

3^3 * 3^2 = (3 * 3 * 3) * (3 * 3)

Now we can use the Product Rule of Exponents and simplify further:

= (3 * 3 * 3 * 3 * 3)
= 3^5

Therefore, 3^3 * 3^2 is equivalent to 3^5.