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How do you rationalize the denominator and simplify #(9w^9)/root4(2Z^7)#?

Answer 1

Abigail Allen

#(9w^9root(4)(8z))/(2z^2)#

You would multiply the terms of the fraction by the factor

#root(4)(2^3z)#

Then

#(9w^9root(4)(2^3z))/(root(4)(2z^7)root(4)(2^3z)#

#=(9w^9root(4)(8z))/(root(4)(2^4z^8)#

#=(9w^9root(4)(8z))/(2z^2)#

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Answer 2

Hazel Anglin

To rationalize the denominator and simplify the expression (9w^9)/√(2Z^7), we can multiply both the numerator and denominator by the conjugate of the denominator.

The conjugate of √(2Z^7) is √(2Z^7).

By multiplying the numerator and denominator by √(2Z^7), we get:

(9w^9 * √(2Z^7))/(√(2Z^7) * √(2Z^7))

Simplifying the denominator:

(9w^9 * √(2Z^7))/(√(2Z^7))^2

Simplifying the denominator further:

(9w^9 * √(2Z^7))/(2Z^7)

The simplified expression is:

(9w^9 * √(2Z^7))/(2Z^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.