Understand Cube Root: We have the expression root(3)(-8a^(11)). First, we need to understand that the cube root of a number is the same as raising that number to the power of 1/3. So, root(3)(-8a^(11)) can be rewritten as (-8a^(11))^(1/3).Deal with Numerical Part: Now, let's deal with the numerical and variable parts separately. For the numerical part, we have the cube root of -8. Since -8 is equal to -2^3, the cube root of -8 is -2.Deal with Variable Part: For the variable part, we have a^(11). When taking the cube root of a variable to an exponent, we divide the exponent by 3. So, a^(11) becomes a^(11/3).Combine Numerical and Variable Parts: Combining the numerical and variable parts, we get: (-2)(a^(11/3)). This is the simplified form of the original expression.

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$\sqrt[3]{-8 a^{11}}$

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Algebra 1

Evaluate integers raised to rational exponents

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\sqrt[3]{-8 a^{11}}

Understand Cube Root: We have the expression $\sqrt[3]{-8a^{11}}$ . First, we need to understand that the cube root of a number is the same as raising that number to the power of $\frac{1}{3}$ . So, $\sqrt[3]{-8a^{11}}$ can be rewritten as $(-8a^{11})^{\frac{1}{3}}$ .
Deal with Numerical Part: Now, let's deal with the numerical and variable parts separately. For the numerical part, we have the cube root of $-8$ . Since $-8$ is equal to $-2^3$ , the cube root of $-8$ is $-2$ .
Deal with Variable Part: For the variable part, we have $a^{11}$ . When taking the cube root of a variable to an exponent, we divide the exponent by $3$ . So, $a^{11}$ becomes $a^{\frac{11}{3}}$ .
Combine Numerical and Variable Parts: Combining the numerical and variable parts, we get: $\newline$ $(-2)(a^{11/3})$ . $\newline$ This is the simplified form of the original expression.