Use the rules of exponents to simplify the expression. write the answer with positive exponents. Assume that all variables represent positive real numbers.

I don't understand,

Step-by-step explanation:

is it true ? first we want to simplify the expression in the numerator. Since the term (x2z) is being raised to the 1/4 power, we multiply the exponents of each variable to give us a simplified power. The denominator is already simplified. This gives us

x2*1/4z1/4/x-1/2z1/2

x1/2z1/4/x-1/2z1/2

To further simplify from this point, we make use of the fact that xA/xB=xA-B. That is, the power of exponential terms divided by terms with the same base is equal to the difference in the exponents. We do this for both x and z.

x1/2-(-1/2)z1/4-1/2

We recognize that the subtraction of a negative term in a power of x leads us to add the two terms, and we find a common denominator, 4, to subtract the powers of z. We find

x1z-1/4

The power of 1 in the x term gives us our base, x, and the power of -1/4 in the z term can be rewritten as a positive exponent in the denominator of our simplified expression. This gives the answer

x/z1/4

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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