Which expression is equal to 5^6?
A. 6×5 B. 36×6×6×6 C. 25×5×5×5 D. 125×125
The Correct Answer and Explanation is:
To determine which expression is equal to (5^6), let’s first clarify what (5^6) means. The expression (5^6) represents the number 5 multiplied by itself six times, which can be written out as:
[
5^6 = 5 \times 5 \times 5 \times 5 \times 5 \times 5
]
Now, let’s evaluate each of the provided options to see which one equals (5^6).
Option A: (6 \times 5)
This equals (30). This is not equal to (5^6).
Option B: (36 \times 6 \times 6 \times 6)
Calculating this step by step:
- (36 \times 6 = 216)
- (216 \times 6 = 1296)
- (1296 \times 6 = 7776)
This value is also not equal to (5^6).
Option C: (25 \times 5 \times 5 \times 5)
Calculating this:
- (25) is equal to (5^2), and (5 \times 5 \times 5) is (5^3). Thus, we can express it as:
[
25 \times 5 \times 5 \times 5 = 5^2 \times 5^3 = 5^{2+3} = 5^5
]
This is not equal to (5^6).
Option D: (125 \times 125)
Calculating this:
- (125) can be expressed as (5^3), thus:
[
125 \times 125 = 5^3 \times 5^3 = 5^{3+3} = 5^6
]
This matches (5^6).
Based on the evaluations, the correct answer is D: (125 \times 125), which equals (5^6).
In summary, each option was evaluated to see if it equaled (5^6). The only expression that accurately represents (5^6) through the laws of exponents was (125 \times 125), as it can be broken down into the form (5^6).