Expand 5 to the Fourth Power: Calculate 5⁴

Exponents with Multiplication Expansion

Expand the following equation:

54= 5^4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Identify the equivalent expressions
00:04 According to the laws of exponents, the multiplication of powers with the same base (A)
00:08 equals the same base raised to the sum of the exponents (N+M)
00:11 We will apply this formula to our exercise in order to simplify it
00:14 We'll maintain the base and add together the exponents
00:18 We can observe that this expression is not equal to the original expression
00:21 Let's simplify the remaining expressions in the same way
00:25 This expression is not equal to the original expression
00:37 This expression is also not equal to the original expression
00:51 This expression is equal to the original expression
00:55 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Expand the following equation:

54= 5^4=

3

Final Answer

5×5×52 5\times5\times5^2

Key Points to Remember

Essential concepts to master this topic
  • Definition: 54 5^4 means multiply 5 by itself 4 times
  • Technique: 54=5×5×5×5=625 5^4 = 5 \times 5 \times 5 \times 5 = 625
  • Check: Count the base factors: 4 fives multiplied together gives 625 ✓

Common Mistakes

Avoid these frequent errors
  • Adding exponents incorrectly when expanding
    Don't write 54 5^4 as 51×52×53 5^1 \times 5^2 \times 5^3 = wrong expansion! This adds exponents (1+2+3=6) instead of using 4 equal factors. Always write 54 5^4 as exactly 4 copies of the base: 5×5×5×5 5 \times 5 \times 5 \times 5 .

Practice Quiz

Test your knowledge with interactive questions

\( 112^0=\text{?} \)

FAQ

Everything you need to know about this question

Why is 5×5×52 5 \times 5 \times 5^2 the correct answer?

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Because 52=5×5 5^2 = 5 \times 5 , so 5×5×52=5×5×(5×5) 5 \times 5 \times 5^2 = 5 \times 5 \times (5 \times 5) gives us exactly 4 copies of 5 multiplied together!

What's wrong with 51×52×53 5^1 \times 5^2 \times 5^3 ?

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This expression actually equals 56 5^6 , not 54 5^4 ! When multiplying powers with the same base, you add the exponents: 1+2+3=6.

How do I know which expansion is correct?

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Count the base factors! 54 5^4 needs exactly 4 copies of 5. Check each option by expanding completely and counting how many 5's you get.

Can I write 54 5^4 in other ways?

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Yes! You could write 52×52 5^2 \times 5^2 or 53×51 5^3 \times 5^1 , but the question asks for an expansion that shows the repeated multiplication structure.

Why not just calculate 625 directly?

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The question asks you to expand the expression, showing the multiplication structure. This helps you understand what exponents really mean before jumping to the final answer!

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