If (x^a / x^b = x^7) and (a+b=13), what is the value of (a)?
Answer and explanation
Correct answer: 10
The governing concept is the quotient law of exponents: for a non-zero base, x^a / x^b = x^(a-b). Therefore the first condition gives a-b=7, while the second condition gives a+b=13. Adding these two equations eliminates b: 2a=20, so a=10. Substitution confirms the result because b=3, and then a-b=10-3=7 and a+b=10+3=13. Thus option C is correct. Option A is the value of b, option B is only the exponent difference, and option D is the given sum rather than the required value of a.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The governing concept is the quotient law of exponents: for a non-zero base, x^a / x^b = x^(a-b). Therefore the first condition gives a-b=7, while the second condition gives a+b=13. Adding these two equations eliminates b: 2a=20, so a=10. Substitution confirms the result because b=3, and then a-b=10-3=7 and a+b=10+3=13. Thus option C is correct. Option A is the value of b, option B is only the exponent difference, and option D is the given sum rather than the required value of a.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
