Which is equivalent to StartFraction left-parenthesis x Superscript 2 Baseline y Superscript negative 2 Baseline right-parenthesis Superscript negative 3 Baseline over left-parenthesis x Superscript negative 2 Baseline y right-parenthesis Superscript negative 2 Baseline EndFraction?
Answer options with 5 options
A.
StartFraction x Superscript 3 Baseline over y Superscript 3 Baseline EndFraction
B.
StartFraction x Superscript 2 Baseline over y Superscript 4 Baseline EndFraction
C.
StartFraction y Superscript 4 Baseline over x Superscript 2 Baseline EndFraction
D.
StartFraction x Superscript 10 Baseline over y Superscript 8 Baseline EndFraction
E.
StartFraction y Superscript 8 Baseline over x Superscript 10 Baseline EndFraction
The expression can be simplified as follows:
StartFraction left-parenthesis x Superscript 2 Baseline y Superscript negative 2 Baseline right-parenthesis Superscript negative 3 Baseline over left-parenthesis x Superscript negative 2 Baseline y right-parenthesis Superscript negative 2 Baseline EndFraction
= (x^2y^(-2))^(-3) / (x^(-2)y)^(-2) (Using the rule (a/b)^c = a^c / b^c)
= (1/(x^2y^2))^(-3) / (1/(x^2y))^(-2) (Using the rule (a^(-b))^c = (1/a^b)^c = 1/(a^bc))
= (x^(-6)y^(-6)) / (x^(-4)y^(-2)) (Using the rule a/b = a^(-1)b)
= x^(-6-(-4))y^(-6-(-2)) (Using the rule a^(-b) = 1/a^b)
= x^(-2)y^(-4)
= StartFraction 1 Over x Superscript 2 Baseline y Superscript 4 Baseline EndFraction
Therefore, the equivalent expression is option B. StartFraction x Superscript 2 Baseline over y Superscript 4 Baseline EndFraction.
u sure
Apologies for the mistake in my previous response. Let's re-evaluate the expression:
StartFraction left-parenthesis x Superscript 2 Baseline y Superscript negative 2 Baseline right-parenthesis Superscript negative 3 Baseline over left-parenthesis x Superscript negative 2 Baseline y right-parenthesis Superscript negative 2 Baseline EndFraction
= (x^2y^(-2))^(-3) / (x^(-2)y)^(-2)
Using the negative exponent rule (a^(-b) = 1/a^b), we can simplify further:
= (1/(x^2y^2))^(-3) / (1/(x^2y))^(-2)
Using the power of a power rule (a^(bc) = (a^b)^c), we can simplify further:
= (1/(x^2y^2))^(-3) / (1/(x^2y^2))^(-2)
Using the rule (a/b)^c = a^c / b^c, we can simplify further:
= (x^2y^2)^2 / (x^2y^2)^3
Using the power rule (a^b * a^c = a^(b+c)), we can simplify further:
= (x^4y^4) / (x^6y^6)
Using the rule a/b = a^(-1) * b, we can simplify further:
= (x^4 / x^6) * (y^4 / y^6)
Using the power rule (a^(-b) = 1/a^b), we can simplify further:
= (1/x^(6-4)) * (1/y^(6-4))
= (1/x^2) * (1/y^2)
Using the rule a/b = a^(-1) * b, we can simplify further:
= (1/(x^2*y^2))
Therefore, the correct equivalent expression is StartFraction 1 Over x Superscript 2 Baseline y Superscript 2 Baseline EndFraction.
I apologize for the confusion caused and appreciate your patience.
but what letter is it?
Apologies for the confusion. The correct equivalent expression, in terms of the original variables, is:
StartFraction 1 Over x Superscript 2 Baseline y Superscript 2 Baseline EndFraction
Therefore, the correct answer is not represented by any of the given options. None of the options provided match the simplified expression.