Answer :

GinnyAnswer
To evaluate the expression [tex]\(\left(\frac{2^2 x^2}{x y^3}\right)^2\)[/tex] for [tex]\(x = 4\)[/tex] and [tex]\(y = 2\)[/tex], we will follow these steps:

1. Substitute the given values into the expression:

[tex]\[ \left(\frac{2^2 \cdot 4^2}{4 \cdot 2^3}\right)^2 \][/tex]

2. Simplify the inner expression:

- Calculate [tex]\(2^2\)[/tex]:

[tex]\[ 2^2 = 4 \][/tex]

- Calculate [tex]\(4^2\)[/tex]:

[tex]\[ 4^2 = 16 \][/tex]

- Calculate [tex]\(2^3\)[/tex]:

[tex]\[ 2^3 = 8 \][/tex]

Now substitute the calculated values back into the expression:

[tex]\[ \left(\frac{4 \cdot 16}{4 \cdot 8}\right)^2 \][/tex]

3. Simplify the fraction inside the parentheses:

- Multiply the numbers in the numerator:

[tex]\[ 4 \cdot 16 = 64 \][/tex]

- Multiply the numbers in the denominator:

[tex]\[ 4 \cdot 8 = 32 \][/tex]

Now we have:

[tex]\[ \left(\frac{64}{32}\right)^2 \][/tex]

4. Simplify the fraction [tex]\(\frac{64}{32}\)[/tex]:

[tex]\[ \frac{64}{32} = 2 \][/tex]

5. Square the result:

[tex]\[ 2^2 = 4 \][/tex]

6. Conclusion:

The evaluated expression [tex]\(\left(\frac{2^2 x^2}{x y^3}\right)^2\)[/tex] for [tex]\(x = 4\)[/tex] and [tex]\(y = 2\)[/tex] is:

[tex]\[ \boxed{4} \][/tex]

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