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sqrt(13x^(6))

$\sqrt{13 x^{6}}$

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Evaluate integers raised to positive rational exponents

Full solution

Q.

\sqrt{13 x^{6}}

Identify Components: Identify the components of the expression. $\newline$ We have the square root of a product: $13$ and $x^{6}$ .
Square Root Function: Recognize that the square root function is the same as raising to the power of $\frac{1}{2}$ . So, $\sqrt{13x^{6}}$ is the same as $(13x^{6})^{\frac{1}{2}}$ .
Apply Power Rule: Apply the power rule for exponents, which states that $(a^{m})^{n} = a^{m*n}$ . $\newline$ In this case, we have $(13^{\frac{1}{2}}) \times (x^{6\times(\frac{1}{2})})$ .
Calculate Exponent: Calculate the exponent for $x$ . $6 \times (\frac{1}{2}) = 3$ , so $x^{6\times(\frac{1}{2})} = x^3$ .
Evaluate Square Root: Evaluate the square root of $13$ . $\newline$ The square root of $13$ cannot be simplified further as $13$ is not a perfect square. So, $13^{1/2}$ remains as is.
Combine Simplified Terms: Combine the simplified terms. $\newline$ The final simplified form is $13^{\frac{1}{2}} \times x^3$ .

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