QuestionAugust 25, 2025

Simplify the following expression by removing as many factors as possible from under the radical. sqrt [5](-1024) sqrt [5](-1024)= square (Simplify your answer.)

Simplify the following expression by removing as many factors as possible from under the radical. sqrt [5](-1024) sqrt [5](-1024)= square (Simplify your answer.)
Simplify the following expression by removing as many factors as possible from under the radical. sqrt [5](-1024) sqrt [5](-1024)= square (Simplify your answer.)

Solution
4.0(293 votes)

Answer

-4 Explanation 1. Identify the expression Recognize that -1024 is a negative number and can be expressed as -1 \times 1024. 2. Simplify the positive part Calculate 1024^{\frac{1}{5}}. Since 1024 = 2^{10}, then 1024^{\frac{1}{5}} = (2^{10})^{\frac{1}{5}} = 2^{2} = 4. 3. Apply the negative sign The fifth root of -1 is -1, so \sqrt[5]{-1} = -1.

Explanation

1. Identify the expression<br /> Recognize that $-1024$ is a negative number and can be expressed as $-1 \times 1024$.<br />2. Simplify the positive part<br /> Calculate $1024^{\frac{1}{5}}$. Since $1024 = 2^{10}$, then $1024^{\frac{1}{5}} = (2^{10})^{\frac{1}{5}} = 2^{2} = 4$.<br />3. Apply the negative sign<br /> The fifth root of $-1$ is $-1$, so $\sqrt[5]{-1} = -1$.
Click to rate:

Similar Questions