# How do you simplify #((4x^2y )/( 3xy^2))^4#?

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To simplify (\left(\frac{4x^2y}{3xy^2}\right)^4), raise each term inside the parentheses to the power of 4:

[\left(\frac{4x^2y}{3xy^2}\right)^4 = \left(\frac{4^4x^{2 \times 4}y^4}{3^4x^4y^{2 \times 4}}\right)]

Simplify the numerator and denominator separately:

Numerator: [4^4 = 256] [x^{2 \times 4} = x^8] [y^4]

Denominator: [3^4 = 81] [x^4] [y^{2 \times 4} = y^8]

Combine the simplified terms:

[\frac{256x^8y^4}{81x^4y^8}]

Now, simplify the expression further by canceling out common factors:

[\frac{256}{81} \times \frac{x^8}{x^4} \times \frac{y^4}{y^8}]

[= \frac{256}{81} \times x^{8-4} \times y^{4-8}]

[= \frac{256}{81} \times x^4 \times y^{-4}]

[= \frac{256x^4}{81y^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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