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How do you simplify #(2x^2y^-5)(-6x^-5y^3)(1/3x^-1y^6)# and write it using only positive exponents?

Answer 1

Avery Alexander

#(-4y^4)/(x^4)#

Use the following 3 Laws of Exponents to simplify the expression:

#a^(-m)=1/a^m#

#(a^m)(a^n)=a^(m+n)#

#a^m/a^n=a^(m-n)#

#(2x^2)(1/y^5)(-6y^3)(1/x^5)(1/3y^6)(1/x)#

#(-12x^2y^3y^6)/(3y^5x^5x)#

#(-4x^2y^9)/(y^5x^6)#

#(-4y^4)/(x^4)#

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Answer 2

Jace Anderson

To simplify the expression ( (2x^2y^{-5})(-6x^{-5}y^3)(\frac{1}{3}x^{-1}y^6) ) and write it using only positive exponents, follow these steps:

Multiply the coefficients: ( 2 \times (-6) \times \frac{1}{3} = -4 ).
Multiply the variables with the same base, adding their exponents: For ( x ): ( 2x^2 \times (-6x^{-5}) \times \frac{1}{3}x^{-1} = \frac{2(-6)}{3}x^{2 + (-5) + (-1)} ) ( = -4x^{-4} )

For ( y ): ( y^{-5} \times y^3 \times y^6 = y^{-5 + 3 + 6} ) ( = y^4 )
Combine the results: ( -4x^{-4}y^4 )

The expression simplified with only positive exponents is ( -4x^{-4}y^4 ).

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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.