Product Rule of Exponents Quick Check
Math 8 Q1 (Pre-Algebra) / Exponent Rules
Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
(5^2)^9
32^7
10^8⋅10^8
6^2⋅7^3
The expression that is correctly developed to use the Product Rule of Exponents is:
10^8⋅10^8.
The correct expression to use the Product Rule of Exponents is 10^8 ⋅ 10^8.
To determine which expression correctly uses the Product Rule of Exponents, we need to understand what the Product Rule is. The Product Rule states that when multiplying two exponential expressions with the same base, we can add their exponents.
Let's analyze each expression to see if it follows the Product Rule:
1. (5^2)^9:
This expression does not use the Product Rule because it involves taking an exponent to an exponent. In this case, we need to raise the base (5) to the product of the two exponents (2 * 9 = 18).
2. 32^7:
This expression does not use the Product Rule because it only has a single exponential term without any multiplication involved.
3. 10^8⋅10^8:
This expression correctly uses the Product Rule since we have two exponential terms with the same base (10) being multiplied. According to the Product Rule, we can add the exponents, resulting in 10^(8 + 8) = 10^16.
4. 6^2⋅7^3:
This expression first involves raising 6 to the 2nd power and 7 to the 3rd power. Since there is no multiplication operation between them, the Product Rule does not apply here.
Based on this analysis, the expression that correctly uses the Product Rule of Exponents is 10^8⋅10^8.