Which expression is equivalent to

Question

(3x^3y^-4)^-2 ?
A. y^8/6x^6
B. y^8/9x^6
C. 6x^-6y^8
D. 9y^8/x^8

Answer 1

To simplify the expression (3x^3y^-4)^-2, we use the exponent rule which states that when you raise a power to a negative exponent, you can rewrite it as the reciprocal raised to the positive exponent.

In this case, we have (3x^3y^-4)^-2. Since the negative exponent is outside the parentheses, we can rewrite the expression as 1/(3x^3y^-4)^2.

Now let's simplify the expression inside the parentheses:
(3x^3y^-4)^2 can be expanded as (3^2)(x^3)^2(y^-4)^2.

Simplifying further, we get:
(3^2)(x^3)^2(y^-4)^2 = 9x^6y^-8.

Finally, substituting this simplified expression back into the original expression, we get:
1/(3x^3y^-4)^2 = 1/(9x^6y^-8).

This can be further simplified by applying the negative exponent rule:
1/(9x^6y^-8) = y^8/(9x^6).

Therefore, the expression is equivalent to option B: y^8/9x^6.