Compare Powers: Which is Larger, 7² or 7³?

Which is larger?

72 ——73 7^2\text{ }_{——}7^3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine which is bigger?
00:03 The bases are equal, therefore the size depends on the exponent
00:07 The larger exponent gives the larger value
00:13 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Which is larger?

72 ——73 7^2\text{ }_{——}7^3

2

Step-by-step solution

Let's solve the problem by calculating each value:

Step 1: Calculate 72 7^2 .
72=7×7=49 7^2 = 7 \times 7 = 49 .

Step 2: Calculate 73 7^3 .
73=7×7×7=343 7^3 = 7 \times 7 \times 7 = 343 .

Step 3: Compare 49 49 and 343 343 .
We can clearly see that 49 49 is less than 343 343 .

Therefore, we have 72<73 7^2 < 7^3 .

The correct comparison sign is < < .

Thus, choice 1 is correct: < < .

3

Final Answer

< <

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\( 11^2= \)

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