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CAHSEE Math Videos 210 videos
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CAHSEE Math 3.5 Algebra and Functions 272 Views
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Description:
Algebra and Functions: Drill Set 3, Problem 5. Simplify the expression.
Transcript
- 00:03
And here's your shmoop du jour.
- 00:07
Simplify 5a to the 8th times the square root of b to the 10th...
- 00:12
times 2 times the square root of a to the 8th times b to the 10th.
- 00:18
Here are the potential answers...
- 00:20
Before we spoil the ending, hit pause and try to solve this baby yourself.
Full Transcript
- 00:26
The trickiest part of this expression is recognizing that when we square root a variable with an exponent...
- 00:33
...the square root has the effect of dividing the exponent in half.
- 00:38
So the square root of b to the 10th becomes b to the 5th, and the square root of a to
- 00:44
the 8th becomes a to the 4th. The product of the coefficients 5 and 2 is
- 00:49
just 5 times 2, or 10.
- 00:51
The second important thing we need to know is that when we multiply monomials with the
- 00:56
same base, we can just add the exponents.
- 01:01
If we group like terms together, the product of the problem is 10 times a to the 8th times
- 01:06
a to the 4th... times b to the 5th times b to the 10th.
- 01:09
8 plus 4 equals 12, and 5 plus 10 equals 15...
- 01:13
...so we have 10 times a to the 12th power time b to the 15th....
- 01:18
...which gives us C.
- 01:20
The greatest thing about performing this mathematical trick is that...
- 01:23
...you can try this one at home.
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