(-3a^{1/4})(9a)^{-3/2}

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- Jun 2nd 2012, 06:36 AMzbest1966rational exponents? Solve please
(-3a

^{1/4})(9a)^{-3/2} - Jun 2nd 2012, 06:53 AMReckonerRe: rational exponents? Solve please
- Jun 2nd 2012, 07:03 AMzbest1966Re: rational exponents? Solve please
I understand the properties but how do you solve it.

- Jun 2nd 2012, 07:25 AMReckonerRe: rational exponents? Solve please
If you understood the properties, I suspect you would not be having difficulties with the problem. By the way, we have nothing to "solve" here, this is not an equation. Rather, we are "simplifying" the expression.

$\displaystyle \left(-3a^{1/4}\right)(9a)^{-3/2}$

$\displaystyle =-3a^{1/4}\cdot9^{-3/2}a^{-3/2}$

$\displaystyle =-\frac{3a^{1/4}}{9^{3/2}a^{3/2}}$

$\displaystyle =-\frac{3a^{1/4}}{27a^{3/2}}$

Now, use the properties $\displaystyle \frac{a^m}{a^n} = a^{m-n}$ and $\displaystyle a^{-n} = \frac1{a^n}$ to finish it:

$\displaystyle =-\frac{a^{-5/4}}{9}=-\frac1{9a^{5/4}}$

As a final step, you may want to convert $\displaystyle a^{5/4}$ to radical form, depending on the problem's instructions. - Jun 2nd 2012, 07:51 AMHallsofIvyRe: rational exponents? Solve please