GMATJenn said:
Hello Everyone....I have a question and the solution...but I don't quite understand it! If anyone knows how to explain it, or has resources that relate to this question, I would be very thankful!
Q. What is the Value of
Thanks for your help everyone!!
I can't quite see ALL of your image.....
But, I have an alternate approach to this problem....
I'll use fractional exponents to represent the problem, and try to explain how the rules for exponents lead to the solution. Remember that an exponent of 1/n indicates the nth root. So, sqrt(x) would be x[sup:2d7ldu2l](1/2)[/sup:2d7ldu2l] using a fractional exponent.
Your problem, using fractional exponents, is this:
[(0.000064)[sup:2d7ldu2l](1/3)[/sup:2d7ldu2l]][sup:2d7ldu2l](1/2)[/sup:2d7ldu2l]
One of the rules for exponents says that when you raise a power to a power, you MULTIPLY the exponents.
Symbolically, (a[sup:2d7ldu2l]m[/sup:2d7ldu2l])[sup:2d7ldu2l]n[/sup:2d7ldu2l] = a[sup:2d7ldu2l]m*n[/sup:2d7ldu2l]
Let's apply that rule:
[(0.000064)[sup:2d7ldu2l](1/3)[/sup:2d7ldu2l]][sup:2d7ldu2l](1/2)[/sup:2d7ldu2l] = [0.000064][sup:2d7ldu2l](1/3)*(1/2)[/sup:2d7ldu2l]
or, [0.000064][sup:2d7ldu2l](1/6)[/sup:2d7ldu2l]
Can we write 0.000064 in exponential form? Let's see....that would be (64 / 1000000)
But 64 is 2[sup:2d7ldu2l]6[/sup:2d7ldu2l] and 1 000 000 is 10[sup:2d7ldu2l]6[/sup:2d7ldu2l]............
So, we have
(2[sup:2d7ldu2l]6[/sup:2d7ldu2l] / 10[sup:2d7ldu2l]6[/sup:2d7ldu2l])[sup:2d7ldu2l](1/6)[/sup:2d7ldu2l]
Another of the rules for exponents says that when you raise a fraction to a power, both the numerator and the denominator are raised to that power. Symbolically, (a/b)[sup:2d7ldu2l]m[/sup:2d7ldu2l] = a[sup:2d7ldu2l]m[/sup:2d7ldu2l] / b[sup:2d7ldu2l]m[/sup:2d7ldu2l]
So, [2[sup:2d7ldu2l]6[/sup:2d7ldu2l] / 10[sup:2d7ldu2l]6[/sup:2d7ldu2l]][sup:2d7ldu2l](1/6)[/sup:2d7ldu2l] = [2[sup:2d7ldu2l]6[/sup:2d7ldu2l]][sup:2d7ldu2l](1/6)[/sup:2d7ldu2l] / [10[sup:2d7ldu2l]6[/sup:2d7ldu2l]][sup:2d7ldu2l](1/6)[/sup:2d7ldu2l]
When you multiply the exponents (because you are raising a power to a power), you'll have this:
2/10
But what is that, in decimal form? It is 0.2.