Question

Select the equivalent expression: (z⁴/6²​)⁻³=?

Choose 1 answer:
A. z​/6⁻¹
B. 6⁶​/z¹²
C. z¹²⋅6⁶

Answer 1

The equivalent expression for (z⁴/6²​)⁻³ is 6⁶/z¹², which is achieved by taking the reciprocal of the given expression and raising it to the power of 3.

Step-by-step explanation:

To find the equivalent expression for (z⁴/6²​)⁻³, we must first recognize that raising a quotient to a negative exponent is equivalent to taking the reciprocal of the quotient and then raising it to the positive exponent. This means that our given expression evaluates to 6⁶/z¹².

Let us perform the operations step by step:

1. Take the reciprocal of the quotient: (z⁴/6²​) becomes (6²/z⁴).
2. Raise the new quotient to the power of 3: (6²³)/(z⁴³).
3. Apply the Power of a Power rule, which states that (a^n)^m = a^(n*m):

The final answer is 6⁶/z¹², which corresponds to choice B.