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$(3x^{3})^{2}$

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Roots of integers

Full solution

Q.

(3x^{3})^{2}

Apply Power of Power Rule: To simplify the expression $3x^{3}$ ^{ $2$ }, we need to 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 $n$ .
Multiply Exponents: Using the power of a power rule, we multiply the exponents. For the coefficient $3$ , which can be considered as $3^{1}$ , we have $(3^{1})^{2} = 3^{1*2} = 3^{2}$ . For the variable $x$ , we have $(x^{3})^{2} = x^{3*2} = x^{6}$ .
Calculate Coefficient Power: Now we calculate the power of the coefficient: $3^{2} = 3 \times 3 = 9$ .
Combine Results: Combine the results to get the final simplified expression: $9x^{6}$ .

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