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How do you express the following using fractional exponents: #4sqrt(xy+6)sqrt(xy-3)#?

Answer 1

Eli Assouline

#color(red)( 4sqrt(xy+6)sqrt(xy-3) = 4((xy+6)(xy-3))^(1/2)#

#4sqrt(xy+6)sqrt(xy-3) = 4(xy+6)^(1/2)(xy-3)^(1/2)#

#x^ay^a = (xy)^a#, so

#(xy+6)^(1/2)((xy-3)^(1/2) = ((xy+6)(xy-3))^(1/2)#

∴ #4sqrt(xy+6)sqrt(xy-3) = 4((xy+6)(xy-3))^(1/2)#

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Answer 2

Savannah Anderson

[ 4\sqrt{xy+6}\sqrt{xy-3} = 4(xy+6)^{\frac{1}{2}}(xy-3)^{\frac{1}{2}} ]

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Answer 3

Eva Adamson

To express ( 4\sqrt{xy+6}\sqrt{xy-3} ) using fractional exponents, we can rewrite each square root as a rational exponent.

( \sqrt{xy+6} ) can be expressed as ( (xy+6)^{\frac{1}{2}} ), and ( \sqrt{xy-3} ) can be expressed as ( (xy-3)^{\frac{1}{2}} ).

Therefore, ( 4\sqrt{xy+6}\sqrt{xy-3} ) can be expressed as ( 4(xy+6)^{\frac{1}{2}}(xy-3)^{\frac{1}{2}} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.