Compare Powers: Which is Larger, 7² or 7³?

Q: Why is $ 7^3 $ bigger than $ 7^2 $ ?

Because exponents tell you how many times to multiply! $ 7^2 = 7 \times 7 = 49 $, but $ 7^3 = 7 \times 7 \times 7 = 343 $. The extra multiplication makes it much larger.

Q: Is this rule true for any base greater than 1?

Yes! When the base is greater than 1, a larger exponent always gives a larger result. For example, \( 5^2 = 25 .

Q: What if the base was between 0 and 1?

Great question! If the base is between 0 and 1 (like 0.5), then larger exponents give smaller results. For instance, $ 0.5^2 = 0.25 > 0.5^3 = 0.125 $.

Q: What's the fastest way to calculate $ 7^3 $ ?

Start with $ 7^2 = 49 $, then multiply by 7 one more time: $ 49 \times 7 = 343 $. This saves time and uses what you already calculated!

Exponent Comparison with Same Base

Which is larger?

$7^2\text{ }_{——}7^3$

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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

Follow each step carefully to understand the complete solution

Understand the problem

Which is larger?

$7^2\text{ }_{——}7^3$

Step-by-step solution

Let's solve the problem by calculating each value:

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

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

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

Therefore, we have $7^2 < 7^3$ .

The correct comparison sign is $<$ .

Thus, choice 1 is correct: $<$ .

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Base Rule: When bases are equal, larger exponent means larger value
Calculation: $7^2 = 49$ and $7^3 = 343$
Check: Compare computed values: 49 < 343, so $7^2 < 7^3$ ✓

Common Mistakes

Avoid these frequent errors

Assuming higher exponents always mean smaller values
Don't think that $7^3$ is smaller just because 3 > 2 = wrong comparison! This confuses the exponent size with the result size. Always calculate the actual values: $7^2 = 49$ and $7^3 = 343$ to compare correctly.

Practice Quiz

Test your knowledge with interactive questions

Which of the following is equivalent to the expression below?

$$ $$ 10,000^1 $$

FAQ

Everything you need to know about this question

Why is $7^3$ bigger than $7^2$ ?

Because exponents tell you how many times to multiply! $7^2 = 7 \times 7 = 49$ , but $7^3 = 7 \times 7 \times 7 = 343$ . The extra multiplication makes it much larger.

Is this rule true for any base greater than 1?

Yes! When the base is greater than 1, a larger exponent always gives a larger result. For example, $5^2 = 25 < 5^3 = 125$ .

What if the base was between 0 and 1?

Great question! If the base is between 0 and 1 (like 0.5), then larger exponents give smaller results. For instance, $0.5^2 = 0.25 > 0.5^3 = 0.125$ .

Do I always need to calculate the exact values?

Not always! Once you understand the pattern, you can use the rule: same base > 1, larger exponent = larger value. But calculating helps you verify and build confidence!

What's the fastest way to calculate $7^3$ ?

Start with $7^2 = 49$ , then multiply by 7 one more time: $49 \times 7 = 343$ . This saves time and uses what you already calculated!

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Compare Powers: Which is Larger, 7² or 7³?

Exponent Comparison with Same Base

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is $7^3$ bigger than $7^2$ ?

Is this rule true for any base greater than 1?

What if the base was between 0 and 1?

Do I always need to calculate the exact values?

What's the fastest way to calculate $7^3$ ?

🌟 Unlock Your Math Potential

More Questions

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Compare Powers: Is 6¹ Greater Than 1⁶?

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Compare (1/2)⁵ and (0.5)⁵: Exploring Exponential Equivalence

Compare Powers: Which is Larger, 7² or 7³?

Exponent Comparison with Same Base

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is 73 7^3 73 bigger than 72 7^2 72?

Is this rule true for any base greater than 1?

What if the base was between 0 and 1?

Do I always need to calculate the exact values?

What's the fastest way to calculate 73 7^3 73?

🌟 Unlock Your Math Potential

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Why is $7^3$ bigger than $7^2$ ?

What's the fastest way to calculate $7^3$ ?