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Fully simplify.

(3xy^(3))^(2)
Answer:

Fully simplify. $\newline$ $\left(3 x y^{3}\right)^{2}$ $\newline$ Answer:

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Relationship between squares and square roots

Full solution

Q. Fully simplify.

\newline

\left(3 x y^{3}\right)^{2}

\newline

Answer:

Apply Power of Power Rule: We have the expression $(3xy^{3})^{2}$ . To simplify, we will apply the power of a power rule, which states that $(a^{m})^{n} = a^{m*n}$ for any real number $a$ and integers $m$ and $n$ . In this case, we will distribute the exponent of $2$ to both the coefficient $3$ and the variable term $xy^{3}$ .
Simplify Coefficient: First, we raise the coefficient $3$ to the power of $2$ : $(3^2) = 9$ .
Simplify Variable Term: Next, we raise the variable term $xy^{3}$ to the power of $2$ . This means we multiply the exponents of $y$ by $2$ , while $x$ , which has an implied exponent of $1$ , will also be squared: $(x^1 \cdot y^{3})^2 = x^{1\cdot2} \cdot y^{3\cdot2} = x^2 \cdot y^6$ .
Combine Results: Now, we combine the results from the previous steps to get the fully simplified expression: $9 \times x^2 \times y^6$ .

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