Another word problem and one on fractional exponents

[kimmy]

I have the following word problem

Mike found a good deal on some golf clubs at an online auction site. The clubs were selling for $238 (CAN). He wanted to find out if this was a good deal, so he checked the newspaper for the current exchange rate. He saw that the Canadian exchange rate was $1.00 US to 1.52 CAN. If Mike decides to buy these clubs, how much U.S. dollars will he pay for them?

Is the equation: 238/1.52=x/1.00 or 238.=1.52x?
Am I even on the right track?


The next question says to simplify the following expression with fractional exponents:

(a^1/3b^1/6)^2 (a^1/3b^2/3)

I got:
(a^2/3b^2/6) (a^1/3)b^2/3)

= a^2/3+1/3 b^2/6+4/6 (2/3 = 4/6)
=a^3/3 b^6/6
=ab

Is this correct?

 

[soroban]

Hello, kimmy!

Nice work with the fractional exponents!

Simplify: \(\displaystyle \;(a^{\frac{1}{3}}b^{\frac{1}{6}})^2\cdot(a^{\frac{1}{3}}b^{\frac{2}{3}})\)

I got: \(\displaystyle \;(a^{\frac{2}{3}}b^{\frac{2}{6}})\cdot (a^{\frac{1}{3}}b^{\frac{2}{3}})\;=\;a^{(\frac{2}{3}+\frac{1}{3})}\cdot b^{(\frac{2}{6}+\frac{4}{6})}\;=\;a^{\frac{3}{3}}\cdot b^{\frac{6}{6}}\;=\;ab\) . . . . Lovely!

 

[kimmy]

Thank You

Thanks....I thought I had it right.