Product Rule of Exponents Quick Check 1 of 5

Question

Which expression is correctly
developed to use the Product
Rule of Exponents? (1 point)
(5 )
2
9
6 ⋅
2 7
3
32
7
10 ⋅
8 10
8

Answer 1

The Product Rule of Exponents states that when you multiply two expressions with the same base, you add their exponents. The rule can be expressed as:

\[ a^m \cdot a^n = a^{m+n} \]

Let's analyze the given expressions to see which one is correctly developed to use the Product Rule of Exponents.

Looking at the provided options:

1. \( (5^2) \cdot (9^{6}) \)
2. \( (2^7) \cdot (3^{2}) \)
3. \( (32^{7}) \cdot (10^{8}) \)
4. \( (8^{10}) \cdot (8) \)

The correct expression that uses the Product Rule of Exponents is:

\[ (8^{10}) \cdot (8^{1}) = 8^{10 + 1} = 8^{11} \]

This shows the Product Rule of Exponents correctly by adding the exponents of the same base (8).

If you meant to ask about which expression among the listed ones was developed correctly using the Product Rule, that would be statement 4:

Answer: \( 8^{10} \cdot 8^{1} \) (which simplifies to \( 8^{11} \)).