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Simplify the expression 28a to the fourth, b to the sixth,

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over 7a to the ninth b.

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So a good place to start here is to just try to kind of

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break this up into things that we can simplify a lot easier.

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So the 28 and 7, we know that 28 is divisible by 7.

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So let's say we break that apart into 28 times-- 28 over

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7-- times-- and then we can break this one apart-- a to

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the fourth over a to the ninth.

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So times a to the fourth over a to the ninth.

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I'm just rewriting what we did here, but I'm writing it as a

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product of three terms instead of just one term over here.

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And then finally, you have this last term over here, b to

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the sixth over b.

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So times b to the sixth over b.

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And if you multiplied all this out, you'd take the product of

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the numerators, you'd get that up there.

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You get the product of the denominators, you'd get this

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right there.

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The whole reason I did that is because each of these terms

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can be simplified pretty easily.

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This 28 over 7, that's easy.

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28 divided by 7 is 4.

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Then we have the a to the fourth

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divided by a to the ninth.

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And when you have an exponent in the denominator, you can

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subtract it from the exponent in the numerator.

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We have the same base, a, that's why I

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grouped it this way.

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So this is going to be equal to a to the 4 minus 9 power.

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What's 4 minus 9?

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It's negative 5.

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4a to the negative 5.

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4 minus 9.

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And the same thing here with the b's.

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Times b.

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6 minus-- you have a 1 here.

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You don't see the 1, but it's there.

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If you just have a b, that's the same thing

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as b to the 1 power.

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So b to the sixth divided by b to the 1 power is b to the

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sixth minus 1, or b to the fifth power.

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And we're done.

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We've simplified the expression.

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If you don't want a negative exponent there, you could say,

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well, this is the same thing as 4 times 1 over a to the

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fifth-- that's the same thing as a to the negative 5; these

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two things are the exact same thing-- times b to the fifth.

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And then this, of course, would be equal to 4 b to the

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fifth, a to the fifth.

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Or you could put 4 b to the fifth over a to the fifth.

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All of these are legitimate ways, but all of these are

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simplified versions of our original expression.

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