Question

for x=2^3 , Y=2^-3 and z=3^-1 , write each expression in simplest form with positive exponents

a. xy

Answer 1

\[xy=2^3\times 2^{-3}=2^{3-3}=2^0=1\]

Answer 2

b. \[\frac{ x }{ y }\]
c. \[x^{2}\]
d. \[\sqrt[10]{z}\]
e. \[\left( x + y \right)^2\]
f.xyz

Answer 3

\[\frac{x}{y}=\frac{2^3}{2^{-3}}=2^{3+3}=2^6\]

Answer 4

how many of these you got?

Answer 5

4 left :)

Answer 6

\[x^2=(2^3)^2=2^6\]

Answer 7

\[\sqrt[10]{z}=\sqrt[10]{3^{-1}}=3^{-\frac{1}{10}}=\frac{1}{\sqrt[10]{3}}\]

Answer 8

\[(x+y)^2=x^2+2xy+y^2=2^6+2+2^{-6}\]

Answer 9

and since \(xy=1\) we have \(xyz=z=3^{-1}\)