What is the simplified form of (5² · 5³) ÷ 5⁴?
Answer and explanation
Correct answer: 5¹
For powers with the same nonzero base, multiplication adds exponents and division subtracts exponents: aᵐ·aⁿ=aᵐ⁺ⁿ and aᵐ÷aⁿ=aᵐ⁻ⁿ. First simplify the numerator: 5²·5³=5⁵. Then divide by 5⁴: 5⁵÷5⁴=5⁵⁻⁴=5¹. Hence option A is correct, and the numerical value is 5. Option B results from stopping after multiplying and forgetting the division. Option C incorrectly adds all three exponents, even though the final operation is division. Option D subtracts in the reverse order, 4−5, rather than numerator exponent minus denominator exponent. Since the common base 5 is nonzero, the exponent laws apply without any restriction problem.
Frequently asked questions
What is the correct answer to this question?
5¹
Why is this the correct answer?
For powers with the same nonzero base, multiplication adds exponents and division subtracts exponents: aᵐ·aⁿ=aᵐ⁺ⁿ and aᵐ÷aⁿ=aᵐ⁻ⁿ. First simplify the numerator: 5²·5³=5⁵. Then divide by 5⁴: 5⁵÷5⁴=5⁵⁻⁴=5¹. Hence option A is correct, and the numerical value is 5. Option B results from stopping after multiplying and forgetting the division. Option C incorrectly adds all three exponents, even though the final operation is division. Option D subtracts in the reverse order, 4−5, rather than numerator exponent minus denominator exponent. Since the common base 5 is nonzero, the exponent laws apply without any restriction problem.
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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