Use the Product Rule of Exponents to simplify the expression 75 ⋅72 .(1 point)
To simplify the expression 75 ⋅ 72 using the Product Rule of Exponents, we first need to express both numbers in terms of prime factors.
Let's start with 75:
75 can be expressed as 3^1 * 5^2, since it is the product of 3 and two 5s.
Next, let's look at 72:
72 can be expressed as 2^3 * 3^2, since it is the product of three 2s and two 3s.
Using the Product Rule of Exponents, which states that when multiplying two numbers with the same base, you add their exponents, we can simplify the expression:
75 ⋅ 72 = (3^1 * 5^2) ⋅ (2^3 * 3^2)
Now, we can apply the Product Rule of Exponents by adding the exponents for each prime factor:
(3^1 * 5^2) ⋅ (2^3 * 3^2) = 3^(1+2) * 5^2 * 2^3
Simplifying further, we have:
3^3 * 5^2 * 2^3
So, the expression 75 ⋅ 72 simplified using the Product Rule of Exponents is 3^3 * 5^2 * 2^3.