Mathematical Expression Comparison: Determining the Greater Value

Exponent Evaluation with Multi-Base Comparison

Which expression is of greater value:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the largest
00:03 A power is writing the multiplication of a number by itself several times
00:06 We'll simplify each power and solve it to find the largest
00:17 And we found that this is the largest expression
00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Which expression is of greater value:

2

Step-by-step solution

Let's solve the problem by evaluating each expression:

  • Calculate 24 2^4 :
    24=2×2×2×2=16 2^4 = 2 \times 2 \times 2 \times 2 = 16 .
  • Calculate 37 3^7 :
    37=3×3×3×3×3×3×3=2187 3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187 .
  • Calculate 102 10^2 :
    102=10×10=100 10^2 = 10 \times 10 = 100 .
  • Calculate 55 5^5 :
    55=5×5×5×5×5=3125 5^5 = 5 \times 5 \times 5 \times 5 \times 5 = 3125 .

Now, let's compare the computed values: 16 16 (for 24 2^4 ), 2187 2187 (for 37 3^7 ), 100 100 (for 102 10^2 ), and 3125 3125 (for 55 5^5 ).

Clearly, the value 3125 3125 is the largest among the values we've calculated.

Therefore, the expression with the greatest value is 55 5^5 .

3

Final Answer

55 5^5

Key Points to Remember

Essential concepts to master this topic
  • Rule: Calculate each power by multiplying the base by itself repeatedly
  • Technique: Compute 55=5×5×5×5×5=3125 5^5 = 5 \times 5 \times 5 \times 5 \times 5 = 3125
  • Check: Compare all calculated values: 16, 2187, 100, and 3125 to find largest ✓

Common Mistakes

Avoid these frequent errors
  • Confusing exponent with multiplication
    Don't calculate 55 5^5 as 5 × 5 = 25! This gives 25 instead of 3125. The exponent tells you how many times to multiply the base by itself. Always multiply the base the correct number of times: 55=5×5×5×5×5 5^5 = 5 \times 5 \times 5 \times 5 \times 5 .

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

How do I remember what an exponent means?

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Think of the exponent as "how many times" you multiply the base by itself. So 37 3^7 means multiply 3 by itself 7 times!

Is there a shortcut for calculating large exponents?

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For small exponents like these, it's best to multiply step by step. You can also use patterns: powers of 2 double each time, and powers of 10 just add zeros.

Why is 55 5^5 bigger than 37 3^7 ?

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Even though 7 is bigger than 5, the base matters more here! 55=3125 5^5 = 3125 while 37=2187 3^7 = 2187 . The larger base (5) overcomes the smaller exponent.

What if I make a calculation mistake?

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Double-check your multiplication at each step! For 55 5^5 : start with 5 × 5 = 25, then 25 × 5 = 125, then 125 × 5 = 625, finally 625 × 5 = 3125.

Do I always need to calculate every option?

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Yes, when comparing expressions! You can't tell which is largest just by looking at the bases and exponents. Calculate each value and then compare the results.

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