3a (-3/2)x2a0b (-3/4)

Question

It should contain only positive exponents with no fractional exponents in the denominator

Answer 1

[3a^(-3/2)][2a⁰b^(-3/4)]

 

 

When we have fractional exponents, we are likely to have radical terms.

 

Here are some rules to remember:

 

x^{(m / n)} = ⁿ√(x^m)

 

x^{(-m / n)} = ⁿ√(1 / (x^m))

 

ⁿ√(xⁿ) = x

 

 

First, we can simplify this expression by adding exponents of common bases and multiply the coefficients.

 

6a^(-3/2)b^(3/4) =

 

6 * √(1 / a³) * ⁴√(b³) =

 

[6 * 1 * ⁴√(b³)] / √(a²) √(a) =

 

(6 * ⁴√(b³)) / (a√a)

 

 

Because we have a radical term in the denominator, we need to rationalized the denominator.  Multiply the numerator and denominator by √a.

 

(6 * ⁴√(b³) * √(a)) / a²