Question

Help with simplifying expressions without negative exponents.

(x^2/3 z^-1/3)^2

Answer 1

I am thinking 1/x4/3 z2/3

Answer 2

Written exponentially. Do we still have 1 as the numerator this is confusing?

Answer 3

\[(x^{2/3} z^{-1/3})^{2}\] Multiply both exponents inside by two:
\[x^{4/3} z^{-2/3}\] To eliminate negative exponents, put the z term in the denominator:
\[\frac{ x^{4/3} }{ z^{2/3} }\]

Answer 4

Is the denominator 2?

Answer 5

Theres no need for a 1 in the numerator because you have a term with a positive exponent, so that term stays on top. Only terms with negative exponents get moved into the denominator.

Answer 6

The exponent on the z term is 2/3

Answer 7

Ok, how did we get 2 as the denominator?

Answer 8

The original exponent on the z is -1/3. Multiplied by 2 is -2/3.

Answer 9

Are you saying that we flip it when it is multiplied by a negative number using the reciprocal?

Answer 10

When the exponent is negative, it moves into the denominator and becomes positive.

Answer 11

Ok, then the both 2 is the denominator for both fractions

Answer 12

If the second fraction is ^2/2 should it just equal z?

Answer 13

I don't understand your confusion. The exponent on the z is 2/3.

Answer 14

I am being asked to write in simplest terms. So I am thinking x^4/2 equals ^2/2 or simply x

Answer 15

It is already in simplest form. x^(4/3) / z^(2/3)

Answer 16

Ok, somehow I got 2 as the denominator, you are correct! Thank you! LOl