Find a number that can replace y in the expression (x4)0= x2/3* xy.
2024
Find a number that can replace y in the expression (x4)0= x2/3* xy.
- A.
-2/3
- B.
2/3
- C.
1
- D.
-4
Attempted by 12 students.
Show answer & explanation
Correct answer: A
Key idea: use exponent rules (a^b)^c = a^{b·c} and a^m · a^n = a^{m+n}.
Simplify the left side: (x^4)^0 = x^{4·0} = x^0.
Simplify the right side: x^{2/3} · x^{y} = x^{2/3 + y}.
Equate exponents (for x ≠ 0): 0 = 2/3 + y, so y = -2/3.
Answer: y = -2/3.