Simplify the expression, write with positive exponents only.

Question

anonymous · Answer

$$\left( 18a ^{1/5} \right)/(2a ^{3/2}) ^{1/2}$$

anonymous · Answer

Start with the bottom.  Whenever you have a power to a power, you simply multiply the powers.  
$$18a^{1/5}/(\sqrt{2}a^{3/4})$$Then, subtract powers
$$18a^{1/5-3/4}/\sqrt{2}$$$$18a^{4/20-15/20}/\sqrt{2}$$$$18a^{-11/20}/\sqrt{2}$$Move the negative power to the bottom.
$$18/(a^{11/20}\sqrt{2})$$
Not sure if you need to rationalize the denominator, but we can go through that if you want.

anonymous · Answer

When you multiply the powers wouldn't it be 1/10 and 3/4? Or is that wrong?

anonymous · Answer

The 2a^(3/2) is the only part that's raised to the 1/2 power.  The numerator stands alone.  Unless there were supposed to be parentheses around the entire fraction.

anonymous · Answer

Yeah the parenthesis is around the entire fraction. I didn't know how to do it on here.

anonymous · Answer

Oh, gotcha.  Then yes, 1/10.  Then simple fraction subtraction, and you do the same steps.

anonymous · Answer

And how did you get the square root of 2? instead of just 2?

anonymous · Answer

When you "distribute" (not really distribution) that 1/2, you have to raise everything separated by a multiplication or division to a 1/2