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Subjects
Class 10MathematicsReal NumbersFundamental Theorem of ArithmeticHardLevel 5
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If (p=2^a\times3^3\times5^2) and (p=5400), what is the value of (a)?

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Answer and explanation

Correct answer: 3

Step 1: Prime factorise 5400. Step 2: (5400=54\times100=2^3\times3^3\times5^2). Step 3: Comparing with the given form gives (a=3).

Related tags

Exponent-ComparisonPrime-FactorisationHard

Frequently asked questions

What is the correct answer to this question?

3

Why is this the correct answer?

Step 1: Prime factorise 5400. Step 2: (5400=54\times100=2^3\times3^3\times5^2). Step 3: Comparing with the given form gives (a=3).

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Fundamental Theorem of Arithmetic.

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  1. 1According to the Fundamental Theorem of Arithmetic, every composite number can be written in which form?
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  3. 3What is the correct prime factorisation of 60?
  4. 4What does uniqueness mean in the Fundamental Theorem of Arithmetic?
  5. 5In the prime factorisation of 84, what is the power of 2?
  6. 6The number (2^3\times3^2) is equal to which number?
  7. 7Which is the prime factorisation of 45?
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