What is the simplified form of \(5^4\cdot5^{-2}\cdot5^3\)?
Answer and explanation
Correct answer: \(5^5\)
When powers with the same base are multiplied, their exponents are added: \(5^4\cdot5^{-2}\cdot5^3=5^{4+(-2)+3}=5^5\). Therefore, option A is correct. Option B incorrectly treats the negative exponent as positive, while option C results from an incomplete combination of the exponents. Exam tip: for the same base, use \(a^m\cdot a^n=a^{m+n}\), keeping the sign of every exponent.
Frequently asked questions
What is the correct answer to this question?
\(5^5\)
Why is this the correct answer?
When powers with the same base are multiplied, their exponents are added: \(5^4\cdot5^{-2}\cdot5^3=5^{4+(-2)+3}=5^5\). Therefore, option A is correct. Option B incorrectly treats the negative exponent as positive, while option C results from an incomplete combination of the exponents. Exam tip: for the same base, use \(a^m\cdot a^n=a^{m+n}\), keeping the sign of every exponent.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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