Which expression is correctly developed to use the Product Rule of Exponents?
(5^2)^9
(5 squared in parentheses to the 9th power)
32^7
(32 to the 7th power)
6^2 ⋅ 7^3
(6 squared times 7 cubed)
10^8 ⋅ 10^8
(10 to the 8th power times 10 to the 8th power)
6^2 ⋅ 7^3
(6 squared times 7 cubed)
Find the numerical equivalent of 10^2 ⋅10^3
10
10^5
1,100
100,000
10^2 ⋅10^3 = 100,000
Find the numerical equivalent of 2^5 (2 to the 5th power) ⋅ 2^-2 (2 to the 2nd power but negative)
128
8
16
2
2^5 (2 to the 5th power) ⋅ 2^-2 (2 to the 2nd power but negative) = 2^(5-2) = 2^3 = 8
The expression that is correctly developed to use the Product Rule of Exponents is:
6^2 ⋅ 7^3 (6 squared times 7 cubed)
The expression that is correctly developed to use the Product Rule of Exponents is:
6^2 ⋅ 7^3
To understand why this is the correct expression, let's first review the Product Rule of Exponents. According to the rule, when multiplying two numbers with the same base, you keep the base and add the exponents.
Now, in the given expression, we have 6^2 ⋅ 7^3. Let's break it down:
6^2 represents "6 squared," which means 6 raised to the power of 2. So, 6^2 = 6 * 6 = 36.
7^3 represents "7 cubed," which means 7 raised to the power of 3. So, 7^3 = 7 * 7 * 7 = 343.
Now, using the Product Rule of Exponents, we can combine these two terms:
6^2 ⋅ 7^3 = 36 * 343 = 12,312.
Therefore, 6^2 ⋅ 7^3 is the correctly developed expression that uses the Product Rule of Exponents.