Which equation below models xª•xᵇ = xª⁺ᵇ?A5³ • 5⁴ = 25⁷B5³ • 5⁴ = 5⁷C5 • 5 • 5 + 5 • 5 • 5 • 5 = 5⁷D5 + 5 + 5 • 5 + 5 + 5 + 5 = 5⁷
Question
Which equation below models xⁿ • xᵐ = x^(n + m)?
A 5³ • 5⁴ = 25⁷
B 5³ • 5⁴ = 5⁷
C 5 • 5 • 5 + 5 • 5 • 5 • 5 = 5⁷
D 5 + 5 + 5 • 5 + 5 + 5 + 5 = 5⁷
Solution
The correct equation that models xª•xᵇ = xª⁺ᵇ is B. 5³ • 5⁴ = 5⁷.
Here's why:
The rule of exponents states that when you multiply two exponents with the same base, you add the exponents. In this case, the base is 5.
So, 5³ • 5⁴ = 5⁷ because 3 (the exponent in 5³) + 4 (the exponent in 5⁴) = 7, which is the exponent in 5⁷.
Therefore, 5³ • 5⁴ = 5⁷ correctly models the equation xª•xᵇ = xª⁺ᵇ.
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