Question 107137
To do this problem, you need to raise each of the individual terms inside the parentheses
to the 4th power. 
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In other words:
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{{{(3*a^2*b^3)^4}}} becomes {{{((3^4)*(a^2)^4*(b^3)^4)}}}
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Now you can recognize that {{{3^4}}} is 3*3*3*3 and this product is 81. So you can substitute
81 in place of {{{3^4}}} and the problem is reduced to:
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{{{81*(a^2)^4* (b^3)^4}}}
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Next look at {{{(a^2)^4}}}. You can get an equivalent form of this by multiplying the exponent
4 by the exponent 2 to get {{{a^8}}}. You can also think of {{{(a^2)^4}}} as being {{{a^2}}}
multiplied by itself 4 times and {{{a^2*a^2*a^2*a^2 = a^8}}}. Substitute this into the
problem and the result is:
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{{{81*a^8*(b^3)^4}}}
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Finally, you can raise {{{(b^3)}}} to the 4th power by multiplying the exponent 4 times
the exponent 3 to get an exponent 12. So {{{(b^3)^4 = b^12}}}. Think:
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{{{b^3*b^3*b^3*b^3 = b^12}}}.
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Substitute this and you get the answer to the problem as:
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{{{81*a^8*b^12}}}
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Hope this helps you to understand the problem and how to solve it.  Good luck on the test ...
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