If (d≠0), what is the correct form of (d^r/d^s)?
Answer and explanation
Correct answer: d^(r-s)
The governing concept is the quotient law of exponents. When nonzero powers with the same base are divided, the exponent in the denominator is subtracted from the exponent in the numerator: d^r/d^s = d^(r−s), provided d≠0. Thus option B is correct. For example, if r=5 and s=2, then d^5/d^2 = d^(5−2)=d^3, which confirms the rule. Option A incorrectly adds the exponents, a rule associated with multiplication of like bases. Option C incorrectly multiplies the exponents, which belongs to raising a power to another power. Option D reverses the subtraction order and generally gives the reciprocal result, so it is not correct.
Frequently asked questions
What is the correct answer to this question?
d^(r-s)
Why is this the correct answer?
The governing concept is the quotient law of exponents. When nonzero powers with the same base are divided, the exponent in the denominator is subtracted from the exponent in the numerator: d^r/d^s = d^(r−s), provided d≠0. Thus option B is correct. For example, if r=5 and s=2, then d^5/d^2 = d^(5−2)=d^3, which confirms the rule. Option A incorrectly adds the exponents, a rule associated with multiplication of like bases. Option C incorrectly multiplies the exponents, which belongs to raising a power to another power. Option D reverses the subtraction order and generally gives the reciprocal result, so it is not correct.
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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