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Choose the correct simplification of the expression [tex]\left(x^2 y\right)^2[/tex].

A. [tex]x^4 y^3[/tex]

B. [tex]x^6 y^6[/tex]

C. [tex]x^4 y^2[/tex]

D. [tex]x y^4[/tex]


Sagot :

To simplify the expression [tex]\(\left(x^2 y\right)^2\)[/tex], we need to distribute the exponent to each factor inside the parentheses. Here's a step-by-step explanation:

1. Identify the components inside the parentheses:
[tex]\[ \left(x^2 y\right)^2 \][/tex]
Here, we have two factors, [tex]\(x^2\)[/tex] and [tex]\(y\)[/tex].

2. Apply the exponent to each factor inside the parentheses separately:
It means raising each factor inside the parentheses to the power of 2.

For [tex]\(x^2\)[/tex]:
[tex]\[ \left(x^2\right)^2 = x^{2 \cdot 2} = x^4 \][/tex]

For [tex]\(y\)[/tex]:
[tex]\[ y^2 = y^{1 \cdot 2} = y^2 \][/tex]

3. Combine the results:
Now we have [tex]\(x^4\)[/tex] and [tex]\(y^2\)[/tex] from the above steps. Putting them together, we get:
[tex]\[ x^4 y^2 \][/tex]

Thus, the correct simplification of the expression [tex]\(\left(x^2 y\right)^2\)[/tex] is [tex]\(\boxed{x^4 y^2}\)[/tex].