Questions: Raising a Product or a Quotient to a Power Simplify each of the following. 27. (-6xy^2)^2

Raising a Product or a Quotient to a Power
Simplify each of the following.
27. (-6xy^2)^2
Transcript text: Raising a Product or a Quotient to a Powe Simplify each of the following. 27. $\left(-6 x y^{2}\right)^{2}$
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Solution

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Solution Steps

Step 1: Apply the Power to Each Factor

The expression given is (6xy2)2\left(-6 x y^{2}\right)^{2}. According to the power of a product rule, (ab)n=anbn(ab)^n = a^n b^n, we apply the exponent to each factor inside the parentheses:

(6xy2)2=(6)2(x)2(y2)2 \left(-6 x y^{2}\right)^{2} = (-6)^{2} \cdot (x)^{2} \cdot (y^{2})^{2}

Step 2: Simplify Each Term

Now, simplify each term separately:

  1. (6)2=36(-6)^{2} = 36
  2. (x)2=x2(x)^{2} = x^{2}
  3. (y2)2=y4(y^{2})^{2} = y^{4}
Step 3: Combine the Simplified Terms

Combine the simplified terms to get the final expression:

36x2y4=36x2y4 36 \cdot x^{2} \cdot y^{4} = 36x^{2}y^{4}

Final Answer

36x2y4 \boxed{36x^{2}y^{4}}

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