Which expression is correctly developed to use the Product Rule of Exponents?(1 point)

Question

Answer choices:
10 to the power of 8 ⋅ 10 to the power of 8
32 to the power of 7
6 to the power of 2 ⋅ 73
(5 to the power of 2) times 9

Answer 1

The Product Rule of Exponents states that when multiplying two powers with the same base, you can add the exponents. This is expressed as:

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

Let's analyze the given choices to see which one correctly applies the Product Rule of Exponents:

1. 10 to the power of 8 ⋅ 10 to the power of 8:

   • This can be simplified using the Product Rule: \[ 10^8 \cdot 10^8 = 10^{8+8} = 10^{16} \]
   • This correctly applies the Product Rule.

2. 32 to the power of 7:

   • This does not involve multiplication of two powers; it is just a single term.

3. 6 to the power of 2 ⋅ 73:

   • Here, 73 is not a power of 6, which means no Product Rule can be applied.

4. (5 to the power of 2) times 9:

   • This expression involves 9, which is not a power of 5. Hence, the Product Rule cannot be applied in this case.

Thus, the only expression that correctly uses the Product Rule of Exponents is:

10 to the power of 8 ⋅ 10 to the power of 8.