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