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How do you simplify #x^-2/(3x^-3y^2)# and write it using only positive exponents?

Answer 1

Hazel Anglin

#x/(3y^2)#

#"using the "color(blue)"law of exponents"#

#•color(white)(x)a^m/a^n=a^((m-n))#

#rArrx^-2/(3x^-3y^2#

#=1/3xxx^-2/x^-3xx1/y^2#

#=1/3xx x^(-2-(-3))/1xx1/y^2#

#=1/3xx x^1/1xx1/y^2#

#=(1xx x xx1)/(3xx1xxy^2#

#=x/(3y^2)#

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Answer 2

Savannah Anderson

To simplify ( \frac{x^{-2}}{3x^{-3}y^2} ) and write it using only positive exponents, you can bring the negative exponents to the denominator by changing their signs:

( \frac{1}{x^2} \times \frac{1}{3x^3y^2} = \frac{1}{3x^2 \times x^3 \times y^2} = \frac{1}{3x^{2+3}y^2} = \frac{1}{3x^5y^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.