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How do you simplify #(sqrt(x^-5) + x^-5 y^7 z^-2) (x^9 y^-2 z^9)#?

Answer 1

Avery Alexander

#x^(13/2)y^-2z^9+x^4y^5z^7#

From the given expression #(sqrt(x^-5)+x^-5y^7z^-2)(x^9y^-2z^9)#

Get the product

#(sqrt(x^-5)+x^-5y^7z^-2)(x^9y^-2z^9)#

#(x^(-5/2)+x^-5y^7z^-2)(x^9y^-2z^9)#

#x^(-5/2)*(x^9y^-2z^9)+(x^-5y^7z^-2)(x^9y^-2z^9)#

#x^(-5/2+9)*(y^-2z^9)+(x^(9-5)y^(7-2)z^(9-2))#

#x^(13/2)y^-2z^9+x^4y^5z^7#

God bless....I hope the explanation is useful.

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Answer 2

Savannah Anderson

To simplify the expression, you can combine like terms:

(sqrt(x^-5) + x^-5 y^7 z^-2) (x^9 y^-2 z^9) = x^9/2 * x^-5 * x^9 * y^7 * y^-2 * z^-2 * z^9 = x^(9/2 - 5 + 9) * y^(7 - 2) * z^(-2 + 9) = x^(13/2) * y^5 * z^7

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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.