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How do you evaluate #\frac { 3^ { 6} - 3^ { 2} } { 9^ { 4} - 9^ { 2} }#?

Answer 1

#(3^6-3^2)/(9^4-9^2) = 1/9#

#(3^6-3^2)/(9^4-9^2) = (3^2(3^4-1))/(9^2(9^2-1))#

#color(white)((3^6-3^2)/(9^4-9^2)) = (3^2color(red)(cancel(color(black)((3^4-1)))))/(3^4color(red)(cancel(color(black)((3^4-1)))))#

#color(white)((3^6-3^2)/(9^4-9^2)) = 3^2/3^4#

#color(white)((3^6-3^2)/(9^4-9^2)) = 1/3^2#

#color(white)((3^6-3^2)/(9^4-9^2)) = 1/9#

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Answer 2

Julia Adams

To evaluate ( \frac{3^6 - 3^2}{9^4 - 9^2} ), you would first simplify the exponents, then perform the arithmetic operations. (3^6) equals 729, (3^2) equals 9, (9^4) equals 6561, and (9^2) equals 81. Then, you substitute these values into the expression and perform the subtraction. Finally, you divide the result of the subtraction of the first pair of exponents by the result of the subtraction of the second pair of exponents.

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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.