Question

Rewrite the expression z/z^(1/3) in the form [zⁿ]. Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).

Answer 1

To rewrite the expression z/z^(1/3) in the form [zⁿ], divide the digit term of the numerator by the digit term of the denominator and subtract the exponents of the exponential terms. The expression z/z^(1/3) can be rewritten as z^(2/3).

Step-by-step explanation:

To rewrite the expression z/z^(1/3) in the form [zⁿ], we can use the rule of division of exponentials. We divide the digit term of the numerator (z) by the digit term of the denominator (z^(1/3)) and subtract the exponents of the exponential terms. The digit term of z is 1, and the digit term of z^(1/3) is 1/3. Therefore, we have z/z^(1/3) = z^(1 - 1/3).

Next, we simplify the exponent by finding a common denominator for 1 and 1/3, which is 3. Subtracting 1/3 from 3/3, we get 2/3. Thus, the expression z/z^(1/3) can be rewritten as z^(2/3).