which expression is a perfect cube?\n12x^{12}y^{18}\n12x^{27}y^{125}\n64x^{15}y^{18}\n64x^{27}y^{125}
which expression is a perfect cube?\n12x^{12}y^{18}\n12x^{27}y^{125}\n64x^{15}y^{18}\n64x^{27}y^{125}
Answer
Explanation:
Step1: Recall perfect - cube rules
A number (a) is a perfect cube if (a = b^3) for some number (b), and for a term of the form (x^n), (x^n) is a perfect cube if (n) is divisible by 3. Also, for a coefficient, check if it is a perfect - cube number.
Step2: Analyze the coefficient and exponents of each option
Option 1: (12x^{12}y^{18})
The coefficient (12) is not a perfect - cube ((2^2\times3)).
Option 2: (12x^{27}y^{125})
The coefficient (12) is not a perfect - cube, and the exponent of (y) ((125)) is not divisible by 3 ((125\div3=\frac{125}{3}\notin\mathbb{Z})).
Option 3: (64x^{15}y^{18})
The coefficient (64 = 4^3) is a perfect - cube. The exponent of (x) is (15) ((15\div3 = 5)) and the exponent of (y) is (18) ((18\div3=6)).
Option 4: (64x^{27}y^{125})
The exponent of (y) ((125)) is not divisible by 3.
Answer:
(64x^{15}y^{18})