If u and v are real numbers, which law of exponents is correct?
Answer and explanation
Correct answer: (uv)^n=u^n v^n
The governing law is the power-of-a-product rule: when a product is raised to a common exponent n, the exponent applies separately to each factor. Thus (uv)^n=u^n v^n. For example, with u=2, v=3, and n=2, the left side is (2·3)^2=6^2=36, while the right side is 2^2·3^2=4·9=36. Therefore option A is correct. Option B wrongly changes multiplication into addition. Option C reverses the product rule and is not generally true; for instance, 2^2·3^2=36 but (2+3)^2=25. Option D combines different exponents without a valid exponent law; multiplication of powers with the same base, not different bases, is where exponents are added.
Frequently asked questions
What is the correct answer to this question?
(uv)^n=u^n v^n
Why is this the correct answer?
The governing law is the power-of-a-product rule: when a product is raised to a common exponent n, the exponent applies separately to each factor. Thus (uv)^n=u^n v^n. For example, with u=2, v=3, and n=2, the left side is (2·3)^2=6^2=36, while the right side is 2^2·3^2=4·9=36. Therefore option A is correct. Option B wrongly changes multiplication into addition. Option C reverses the product rule and is not generally true; for instance, 2^2·3^2=36 but (2+3)^2=25. Option D combines different exponents without a valid exponent law; multiplication of powers with the same base, not different bases, is where exponents are added.
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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