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Answer :
To simplify the expression [tex]\((2x^2y)^3\)[/tex], you can follow these steps:
1. Understand the expression: [tex]\((2x^2y)^3\)[/tex] means that you are raising everything inside the parentheses to the power of 3. This includes the coefficient 2 and each variable with its exponent.
2. Apply the power to the coefficient: First, take the number 2 and raise it to the power of 3:
[tex]\[
2^3 = 8
\][/tex]
3. Apply the power to the variable [tex]\(x^2\)[/tex]: Next, apply the exponent to [tex]\(x^2\)[/tex]. When raising a power to another power, you multiply the exponents:
[tex]\[
(x^2)^3 = x^{2 \times 3} = x^6
\][/tex]
4. Apply the power to the variable [tex]\(y\)[/tex]: Similarly, raise [tex]\(y\)[/tex] to the power of 3:
[tex]\[
(y)^3 = y^3
\][/tex]
5. Combine the results: Now, combine all these results to get the final simplified expression:
[tex]\[
8x^6y^3
\][/tex]
So, the simplified form of the expression [tex]\((2x^2y)^3\)[/tex] is [tex]\(8x^6y^3\)[/tex].
1. Understand the expression: [tex]\((2x^2y)^3\)[/tex] means that you are raising everything inside the parentheses to the power of 3. This includes the coefficient 2 and each variable with its exponent.
2. Apply the power to the coefficient: First, take the number 2 and raise it to the power of 3:
[tex]\[
2^3 = 8
\][/tex]
3. Apply the power to the variable [tex]\(x^2\)[/tex]: Next, apply the exponent to [tex]\(x^2\)[/tex]. When raising a power to another power, you multiply the exponents:
[tex]\[
(x^2)^3 = x^{2 \times 3} = x^6
\][/tex]
4. Apply the power to the variable [tex]\(y\)[/tex]: Similarly, raise [tex]\(y\)[/tex] to the power of 3:
[tex]\[
(y)^3 = y^3
\][/tex]
5. Combine the results: Now, combine all these results to get the final simplified expression:
[tex]\[
8x^6y^3
\][/tex]
So, the simplified form of the expression [tex]\((2x^2y)^3\)[/tex] is [tex]\(8x^6y^3\)[/tex].
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