SOLUTION: How do I simplify (3a^2b^3)^4. Someone please help me I have a test coming up soon. Thank You, Ty

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: How do I simplify (3a^2b^3)^4. Someone please help me I have a test coming up soon. Thank You, Ty      Log On


   

Question 107137: How do I simplify (3a^2b^3)^4. Someone please help me I have a test coming up soon.
Thank You,
Ty
Found 2 solutions by edjones, bucky:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
When you have an exponent to an exponent multiply the exponents.
(3a^2b^3)^4
=81a^8b^12
Ed

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
To do this problem, you need to raise each of the individual terms inside the parentheses
to the 4th power.
.
In other words:
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%283%2Aa%5E2%2Ab%5E3%29%5E4 becomes %28%283%5E4%29%2A%28a%5E2%29%5E4%2A%28b%5E3%29%5E4%29
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Now you can recognize that 3%5E4 is 3*3*3*3 and this product is 81. So you can substitute
81 in place of 3%5E4 and the problem is reduced to:
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81%2A%28a%5E2%29%5E4%2A+%28b%5E3%29%5E4
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Next look at %28a%5E2%29%5E4. You can get an equivalent form of this by multiplying the exponent
4 by the exponent 2 to get a%5E8. You can also think of %28a%5E2%29%5E4 as being a%5E2
multiplied by itself 4 times and a%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2+=+a%5E8. Substitute this into the
problem and the result is:
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81%2Aa%5E8%2A%28b%5E3%29%5E4
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Finally, you can raise %28b%5E3%29 to the 4th power by multiplying the exponent 4 times
the exponent 3 to get an exponent 12. So %28b%5E3%29%5E4+=+b%5E12. Think:
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b%5E3%2Ab%5E3%2Ab%5E3%2Ab%5E3+=+b%5E12.
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Substitute this and you get the answer to the problem as:
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81%2Aa%5E8%2Ab%5E12
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Hope this helps you to understand the problem and how to solve it. Good luck on the test ...
.