# How do you simplify #((a^-2b^4c^5)/(a^-4b^-4c^3))^2#?

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To simplify the expression ( \left(\frac{a^{-2}b^4c^5}{a^{-4}b^{-4}c^3}\right)^2 ), use the properties of exponents:

First, distribute the exponent outside the parentheses to each term inside:

[ \left(a^{-2}b^4c^5 \cdot a^{4}b^{4}c^{-3}\right)^2 ]

Now, simplify the expression inside the parentheses by multiplying like bases and adding exponents:

[ a^{-2+4}b^{4+4}c^{5-3} ]

[ a^{2}b^{8}c^{2} ]

Now, raise each term to the power of 2:

[ (a^{2})^2(b^{8})^2(c^{2})^2 ]

[ a^{4}b^{16}c^{4} ]

So, the simplified expression is ( a^{4}b^{16}c^{4} ).

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To simplify the expression ((\frac{a^{-2}b^4c^5}{a^{-4}b^{-4}c^3})^2), use the properties of exponents and perform the necessary operations inside the parentheses first.

- Combine the like terms in the numerator and denominator:

(\frac{a^{-2}b^4c^5}{a^{-4}b^{-4}c^3} = a^{-2-(-4)}b^{4-(-4)}c^{5-3} = a^{2}b^{8}c^{2})

- Now, raise the simplified expression to the power of 2:

((a^{2}b^{8}c^{2})^2 = a^{2*2}b^{8*2}c^{2*2} = a^{4}b^{16}c^{4})

So, the simplified form of ((\frac{a^{-2}b^4c^5}{a^{-4}b^{-4}c^3})^2) is (a^4b^{16}c^4).

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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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