Fully simplify. (3xy^(3))^(2) 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 * y^(3))^2 = x^(1*2) * y^(3*2) = x^2 * y^6.Combine Results: Now, we combine the results from the previous steps to get the fully simplified expression: 9 * x^2 * y^6.

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

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Grade 8

Relationship between squares and square roots

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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: $9 \times x^2 \times y^6$ .