Question

22y⁶z⁸/2y²z⁻⁷

When simplified, the result can be written in the form xyᵇzᶜ, where x is the coefficient, b is the exponent on the variable y, and c is the exponent on the variable z. Find the values of x, b, and c.
A.z^⁻7
B.2y⁴z
C.2y⁴z−7
D.2y²z

Answer 1

To simplify the expression 22y⁶z⁸/2y²z⁻⁷, we subtract the exponents of like bases and divide the coefficients. The correct simplified expression is 11y⁴z³⁵, which does not match any provided answer options, pointing to a potential typo in the question or answers.

Step-by-step explanation:

To simplify the expression 22y⁶z⁸ divided by 2y²z⁻⁷, we can use the laws of exponents which dictate how to simplify terms with the same base. We subtract the exponents of the terms. Hence, we subtract the exponents of y in the numerator (6) and the denominator (2) to get 6 - 2 = 4 for y, and 8 - (-7) = 8 + 7 = 15 for z, since subtracting a negative is the same as adding a positive.

For the coefficients (the numbers in front of the variables), we simply divide 22 by 2 which gives us 11. Thus, the simplified form of the given expression would be 11y⁴z³⁵.

However, the given answer options do not include an option with 11 as a coefficient. Therefore, it seems there might have been a typo or mistake in the provided options or the original expression. Given this discrepancy, the closest correct answer among the provided options is B.2y⁴z³⁵, which incorrectly has a coefficient of 2 instead of 11 and an exponent of 15 for z instead of negative 7.