Which of the expressions is not equivalent to 1/25?
A. 5^3×5^-5
B. 5^-1×5^-1
C. 5^-3×5
D. 5^-2×5^4
Online, “*” is used to indicate multiplication to avoid confusion with “x” as an unknown.
1/25 = 5^-2
When multiplying a particular number, you add the exponents.
C) 5^-3 x 5. Is not equivalent to 1/25
Well, well, well, someone's having a math party! Let me put on my mathematician's hat. Now, let me see here. We're looking for an expression that is NOT equivalent to 1/25.
A. 5^3 × 5^-5. Phew, that's a lot of exponent action going on. Let's break it down. 5^3 is 5 × 5 × 5, and 5^-5 is 1/(5 × 5 × 5 × 5 × 5). Simplifying it, we get 1/125. Nope, that's not equal to 1/25.
B. 5^-1 × 5^-1. Ah, this one looks simpler. 5^-1 is just 1/5, and multiplying two of those gives us (1/5) × (1/5), which is 1/25. So, this one is equivalent to 1/25.
C. 5^-3 × 5. Alright, let's break it down again. 5^-3 is 1/(5 × 5 × 5), and multiplying that by 5 gives us (1/(5 × 5 × 5)) × 5, which simplifies to 1/25. Ah, that's equivalent to 1/25 as well.
D. 5^-2 × 5^4. Hold on, let me do some more calculations. 5^-2 is 1/(5 × 5), and 5^4 is 5 × 5 × 5 × 5. Multiplying those together gives us (1/(5 × 5)) × (5 × 5 × 5 × 5). Simplifying it, we get 1/25. So, it's equivalent to 1/25.
Well, look at that! It seems like all of the given expressions are equivalent to 1/25. So, the answer is "E: None of the above." Keep those math problems coming!
To determine which of the expressions is not equivalent to 1/25, we need to simplify each expression and compare it to 1/25.
Let's simplify each expression one by one:
A. 5^3 × 5^-5
To simplify this expression, we can use the exponent rules. When we multiply powers with the same base, we add their exponents. Therefore, 5^3 × 5^-5 simplifies to 5^(3 + (-5)) = 5^(-2).
B. 5^-1 × 5^-1
Again, using the exponent rules, when we multiply powers with the same base, we add their exponents. So, 5^-1 × 5^-1 simplifies to 5^(-1 + (-1)) = 5^(-2).
C. 5^-3 × 5
Following the exponent rules, when we multiply powers with the same base, we add their exponents. So, 5^-3 × 5 simplifies to 5^(-3 + 1) = 5^(-2).
D. 5^-2 × 5^4
Using the exponent rules, when we multiply powers with the same base, we add their exponents. So, 5^-2 × 5^4 simplifies to 5^(-2 + 4) = 5^2.
Now, let's check which of these expressions is equivalent to 1/25:
1/25 is the same as 5^(-2).
Comparing the simplified expressions to 5^(-2) = 1/25, we can see that options A, B, and C are all equal to 1/25. However, option D, 5^2, is not equivalent to 1/25.
Therefore, the expression that is not equivalent to 1/25 is D. 5^-2 × 5^4.