Question

How do I simplify (a^1/2b)^1/2(ab^1/2)

Answer 1

First distribute the exponent to the upper right of the first parenthesis (1/2), by raising each term inside to the power shown of 1/2. Note that when raising a variable with an existing exponent to another exponent, the exponents should be multiplied. So a1/2 raised to 1/2 equals a 1/2*1/2 or a1/4. The resulting expression is as follows: a1/4b1/2ab1/2

Next reorder to bring "like" variables together: a1/4ab1/2b1/2

Finally complete the multiplication of "like" variables by adding the exponents: a(1/4+1)b(1/2+1/2)

Since 1/4 + 1=4/4+1/4=5/4 and 1/2+1/2=1, the final result is a5/4b

Answer 2

Is that helpful

Answer 3

A little bit

Answer 4

ok

Answer 5

Thank you

Answer 6

\(\bf \large{ \cfrac{a^{\frac{1}{2}}b}{ab^{\frac{1}{2}}}\\ \quad \\
\textit{keeping in mind that}\quad \cfrac{1}{a^n}=a^{-n}\quad \textit{we could say that}\\ \quad \\
\cfrac{a^{\frac{1}{2}}b}{ab^{\frac{1}{2}}}\implies \implies a^{\frac{1}{2}}a^{-1}b^1\cdot b^{-\frac{1}{2}}\\ \quad \\
\textit{recall that }\quad x^n\cdot x^m\implies x^{n+m}}\)

Answer 7

hmm... shoot... missed one thing.. anyhow ehhe

Answer 8

But it's in parenthesis not a fraction...my first problem was like that but I solved that one

Answer 9

I see

Answer 10

ok

Answer 11

\(\bf \large {\left(a^{\frac{1}{2}}b\right)^{\frac{1}{2}}\left(ab^{\frac{1}{2}}\right)\\ \quad \\
\textit{recalling that }\quad (x^n)^m\implies x^{n\cdot m}\\ \quad \\
\left(a^{\frac{1}{2}}b\right)^{\frac{1}{2}}\left(ab^{\frac{1}{2}}\right)\implies a^{\frac{1}{2}\cdot \frac{1}{2}}b^{\frac{1}{2}}ab^{\frac{1}{2}}\implies a^{\frac{1}{2}\cdot \frac{1}{2}}a^1b^{\frac{1}{2}}b^{\frac{1}{2}}\\ \quad \\
a^{\frac{1}{2}\cdot \frac{1}{2}+1}b^{\frac{1}{2}+\frac{1}{2}}}\)

Answer 12

Thank you

Answer 13

yw