SOLUTION: Describe two laws of exponents and provide an example illustrating each law. Explain how to simplify your expression. How do the laws work with rational exponents? Provide a expres

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Question 250287: Describe two laws of exponents and provide an example illustrating each law. Explain how to simplify your expression. How do the laws work with rational exponents? Provide a expression to simplify that includes rational (fractional) exponents.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29

example:

%282%5E4%29%5E2+=+2%5E%284%2A2%29+=+2%5E8+=+256

2%5E4+=+2%2A2%2A2%2A2



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a%5E%28b%2Fc%29+=+%28a%5Eb%29%5E%281%2Fc%29+=+a%5E%28b%2A%281%2Fc%29%29

the fractional exponents from left to right are b%2Fc, 1%2Fc, 1%2Fc.

this can also be expressed as:

a%5E%28b%2Fc%29+=+%28a%5E%281%2Fc%29%29%5Eb+=+a%5E%28%281%2Fc%29%2Ab%29 which is equivalent to a%5E%28b%2A%281%2Fc%29%29

the fractional exponents from left to right are b%2Fc, 1%2Fc, 1%2Fc, 1%2Fc

example:



the fractional exponents from left to right are 4%2F2, 1%2F2, 1%2F2, 1%2F2.

2%5E4+=+16
16%5E%281%2F2%29+=+root%282%2C16%29+=+4

the fractional exponent is 1%2F2

2%5E%281%2F2%29+=+root%282%2C2%29
%28root%282%2C2%29%29%5E4+=+4

the fractional exponent is 1%2F2

a%5E%281%2Fc%29+=+root%28c%2Ca%29.

the fractional exponent is 1%2Fc.

example:

16%5E%281%2F2%29+=+root%282%2C16%29+=+4.

the fractional exponent is 1%2F2.
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a%5E%28b%2Fc%29+=+%28root%28c%2Ca%29%29%5Eb+=+root%28c%2Ca%5Eb%29.

the fractional exponent is b%2Fc.

example:

2%5E%284%2F2%29+=+%28root%282%2C2%29%29%5E4+=+root%282%2C2%5E4%29 = 4.

the fractional exponent is %284%2F2%29.

you can take 2%5E4+=+16 first and then apply 16%5E%281%2F2%29+=+4.

the fractional exponent is 1%2F2.

or:

you can take 2%5E%281%2F2%29+=+sqrt%282%2C2%29 first and then apply sqrt%282%2C2%29%5E4+=+4.

the fractional exponent is 1%2F2.

either way you get the same answer (4).