Use the law of exponents to rewrite and simplify the expression.
$x {(3 x^{2})}^{3}$

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Solution

Simplify the expression:
Consider the given expression.
$x {(3 x^{2})}^{3}$
Using the exponent property $\begin{array}{rcl} {(a^{m})}^{n} & = & a^{m n} \end{array}$ ,
$\begin{array}{rcl} x {(3 x^{2})}^{3} & = & x \times 3^{1 \times 3} \times x^{2 \times 3} \\ \Rightarrow & x {(3 x^{2})}^{3} = x \times 3^{3} \times x^{6} \\ \Rightarrow & x {(3 x^{2})}^{3} = x \times 27 \times x^{6} \end{array}$
Arrange the expression as,
$x {(3 x^{2})}^{3} = 27 \times x \times x^{6}$
Using the exponent property $\begin{array}{rcl} a^{m} \times a^{n} & = & a^{m + n} \end{array}$ ,
$\begin{array}{rcl} x {(3 x^{2})}^{3} & = & 27 \times x^{1 + 6} \\ \Rightarrow & x {(3 x^{2})}^{3} = 27 \times x^{7} \\ \Rightarrow & x {(3 x^{2})}^{3} = 27 x^{7} \end{array}$
Hence, the simplified expression is $27 x^{7}$ .

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