# How do you simplify #(a^ -6) * (b^ 2) / (a^ -3) * (b^8)#?

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To simplify ( \frac{{a^{-6} \cdot b^2}}{{a^{-3} \cdot b^8}} ), we can use the properties of exponents. First, we apply the quotient rule for exponents, which states that ( \frac{a^m}{a^n} = a^{m-n} ). Applying this rule to the numerator and denominator separately, we get ( a^{-6} \cdot b^2 = a^{-6 - (-3)} ) and ( a^{-3} \cdot b^8 = a^{-3 - (-3)} ). Simplifying the exponents, we get ( a^{-6} \cdot b^2 = a^{-3} ) and ( a^{-3} \cdot b^8 = a^{0} ). Since ( a^0 = 1 ) for any nonzero value of ( a ), the expression simplifies to ( b^2 ).

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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.

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.

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.

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