If 2^a = 32 and 8^b = 64, what is the value of a^b - b^a?
Answer and explanation
Correct answer: -7
Use the law of exponents by expressing both equations with a common base. Since 32 = 2^5, the equation 2^a = 2^5 gives a = 5. Also, 8 = 2^3 and 64 = 2^6, so 8^b = (2^3)^b = 2^(3b) = 2^6; hence 3b = 6 and b = 2. Substituting these values, a^b - b^a = 5^2 - 2^5 = 25 - 32 = -7. Therefore option A is correct. Option B has the opposite sign, while 9 and 13 do not follow from the required exponent calculation.
Frequently asked questions
What is the correct answer to this question?
-7
Why is this the correct answer?
Use the law of exponents by expressing both equations with a common base. Since 32 = 2^5, the equation 2^a = 2^5 gives a = 5. Also, 8 = 2^3 and 64 = 2^6, so 8^b = (2^3)^b = 2^(3b) = 2^6; hence 3b = 6 and b = 2. Substituting these values, a^b - b^a = 5^2 - 2^5 = 25 - 32 = -7. Therefore option A is correct. Option B has the opposite sign, while 9 and 13 do not follow from the required exponent calculation.
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.
