How Do I Simplify This Problem?

[ondverg]

I need to know how to simplify this problem: u(to the 2nd power) v(to the 5th power) over uv(to the 4th power). Thanks

 

[mmm4444bot]

You could use a couple properties of exponents.

Here's a similar example that shows how.

(a^7 * b^15)/(a*b)^3

In the denominator, both of the factors (a and b) get cubed. That's according to this property:

(xy)^n = x^n * y^n

(a^7 * b^15)/(a^3 * b^3)

We can factor this ratio into a product of two ratios where the bases are the same in the numerator and denominator.

a^7/a^3 * b^15/b^3

Now, we can use another property of exponents, since the bases are the same on top and bottom, in each ratio of powers above. Here's the property.

a^n/a^m = a^(n - m)

In other words, when the bases are the same in a ratio of powers, we can subtract the lower exponent away from the upper exponent.

a^(7 - 3) * b^(15 - 3)

a^4 * b^12

Your exercise can be done using the same strategy.

MY EDITS: Corrected two typographical errors, neither of which changes the meaning of my post.

 

[ondverg]

Thank you!