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How do you get rid of the negative exponents in #(-4a ^ { 3} b ^ { - 5} ) ^ { - 2}#?

Answer 1

Ethan Adkins

There are two rules we may use here:

Negative exponent rule

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

Multiplying powers

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

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Answer 2

Genesis Allen

To get rid of the negative exponents in the expression ((-4a^3b^{-5})^{-2}), you can apply the negative exponent rule, which states that (a^{-n} = \frac{1}{a^n}).

So, first, we'll rewrite the expression with positive exponents: [\frac{1}{(-4a^3b^{-5})^2}]

Then, we'll square both the numerator and the denominator: [\frac{1}{16a^6b^{-10}}]

Finally, since (b^{-10}) can be written as (b^{10}) in the denominator: [\frac{1}{16a^6b^{10}}]

Therefore, the expression with the negative exponents removed is (\frac{1}{16a^6b^{10}}).

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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.