Question

How do I simplify rational exponents?
Such as, \[{a}^{1/2}({a}^{3/2}-{2a}^{1/2})\]

Answer 1

When you distribute things, you get \(\large a^{3/2+ 1/2} - 2a^{1/2+1/2}\). What do you get when you simplify that? :-)

Answer 2

first multiply through and then deal with the exponents. of course in multiplying, you will be dealing with the exponents, too but in a different way.

Answer 3

\(\bf \Large{ a^{\frac{1}{2}}\left(a^{\frac{3}{2}}-2a^{\frac{1}{2}}\right)\implies a^{\frac{1}{2}}\cdot a^{\frac{3}{2}}-a^{\frac{1}{2}}\cdot 2a^{\frac{1}{2}}\\ \quad \\
\implies a^{\frac{1}{2}+\frac{3}{2}}-a^{\frac{1}{2}+\frac{1}{2}}}\)

Answer 4

hmm got a missing 2 =) \(\bf \Large{ a^{\frac{1}{2}}\left(a^{\frac{3}{2}}-2a^{\frac{1}{2}}\right)\implies a^{\frac{1}{2}}\cdot a^{\frac{3}{2}}-a^{\frac{1}{2}}\cdot 2a^{\frac{1}{2}}\\ \quad \\
\implies a^{\frac{1}{2}+\frac{3}{2}}-2a^{\frac{1}{2}+\frac{1}{2}}}\)

Answer 5

hmmm