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Simplify ${(2w^{3})^{6}}$

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Evaluate integers raised to positive rational exponents

Full solution

Q. Simplify

{(2w^{3})^{6}}

Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . Here, we have $(2w^{3})^{6}$ , so we need to apply the power to both the coefficient $2$ and the variable $w$ raised to the power of $3$ . $\newline$ $(2w^{3})^{6} = 2^{6} \times (w^{3})^{6}$
Calculate Coefficient Power: Calculate the power of the coefficient. $2^{6}$ means $2$ multiplied by itself $6$ times. $2^{6} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64$
Apply Variable Power Rule: Apply the power of a power rule to the variable. $\newline$ $(w^{3})^{6}$ means $w$ raised to the power of $3$ multiplied by itself $6$ times, which is $w$ raised to the power of $3\times6$ . $\newline$ $(w^{3})^{6} = w^{3\times6} = w^{18}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ Now we combine the coefficient and the variable with its new exponent. $\newline$ $64 \times w^{18}$

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