Simplify the expression. Write the answer with positive exponents. Assume all variables represent positive numbers.

(x

^{2}z)^{1/4}/x^{-1/2}z^{1/2}Simplify the expression. Write the answer with positive exponents. Assume all variables represent positive numbers.

(x^{2}z)^{1/4}/x^{-1/2}z^{1/2}

Tutors, please sign in to answer this question.

Cambridge, MA

(x^{2}z)^{1/4}/x^{-1/2}z^{1/2}

First we want to simplify the expression in the numerator. Since the term (x^{2}z) 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

x^{2*1/4}z^{1/4}/x^{-1/2}z^{1/2}

x^{1/2}z^{1/4}/x^{-1/2}z^{1/2}

To further simplify from this point, we make use of the fact that x^{A}/x^{B}=x^{A-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.

x^{1/2-(-1/2)}z^{1/4-1/2}

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

x^{1}z^{-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/z^{1/4}

Bethmarie M.

Superb Mathematics/ELA Tutor: Regents/NYS Test Common Core

Jamaica, NY

5.0
(3 ratings)

Nikunj P.

Math and Science Specialist, Over 14 Years of Educational Experience

Scarsdale, NY

4.9
(186 ratings)

Daisy C.

Effective ELA Tutor - Boston College Graduate - Masters Degree ELA/ESL

Atlantic Beach, NY

5.0
(131 ratings)

- Math Help 5187
- Algebra 4899
- Math Word Problem 4241
- Calculus 2162
- Word Problem 4940
- Algebra 2 3294
- Algebra 1 3929
- Math Problem 970
- Math Help For College 1357
- Math Equations 936