Identify Cube Root: We need to simplify the cube root of -243m^3. First, let's identify the cube root of -243 and m^3 separately. The cube root of -243 is -3 because (-3)^3 = -27 * 9 = -243. The cube root of m^3 is m because m^3 raised to the power of 1/3 is m^(3*(1/3)) = m^1 = m.Calculate Cube Roots: Now, we combine the cube roots of the numbers and the variable. The cube root of -243m^3 is the cube root of -243 times the cube root of m^3. So, root(3)(-243m^3) = root(3)(-243) * root(3)(m^3) = -3 * m.Check for Errors: We check for any mathematical errors in the previous steps. The cube root of a negative number is negative, and the cube root of a variable raised to the third power is the variable itself. No mathematical errors were made.

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$\sqrt[3]{-243 m^{3}}$ =

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Math Problems

Algebra 2

Simplify the product of two radical expressions having same variable

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\sqrt[3]{-243 m^{3}}

Identify Cube Root: We need to simplify the cube root of $-243m^3$ . $\newline$ First, let's identify the cube root of $-243$ and $m^3$ separately. $\newline$ The cube root of $-243$ is $-3$ because $(-3)^3 = -27 \times 9 = -243$ . $\newline$ The cube root of $m^3$ is $m$ because $m^3$ raised to the power of $1/3$ is $-243$ $0$ .
Calculate Cube Roots: Now, we combine the cube roots of the numbers and the variable. $\newline$ The cube root of $-243m^3$ is the cube root of $-243$ times the cube root of $m^3$ . $\newline$ So, $\sqrt[3]{-243m^3} = \sqrt[3]{-243} \times \sqrt[3]{m^3} = -3 \times m$ .
Check for Errors: We check for any mathematical errors in the previous steps. $\newline$ The cube root of a negative number is negative, and the cube root of a variable raised to the $3^{\text{rd}}$ power is the variable itself. $\newline$ No mathematical errors were made.