Identify base and exponent: Identify the base and the exponent. In the expression (-3)^(0.5), -3 is the base raised to the exponent 0.5. Base: -3 Exponent: 0.5Understand exponent 0.5: Understand the meaning of the exponent 0.5. The exponent 0.5 is equivalent to the square root. Therefore, (-3)^(0.5) is the same as the square root of -3.Evaluate square root: Evaluate the square root of a negative number. The square root of a negative number is not a real number; it is an imaginary number. Therefore, the square root of -3 is an imaginary number.Write final answer: Write the final answer using the imaginary unit i. The square root of -3 can be written as sqrt(3) * i, where i is the imaginary unit. Final Answer: sqrt(3) * i

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$(-3)^{0.5}=$

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Grade 8

Powers with negative bases

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(-3)^{0.5}=

Identify base and exponent: Identify the base and the exponent. $\newline$ In the expression $(-3)^{0.5}$ , $-3$ is the base raised to the exponent $0.5$ . $\newline$ Base: $-3$ $\newline$ Exponent: $0.5$
Understand exponent $0$ . $5$ : Understand the meaning of the exponent $0.5$ . The exponent $0.5$ is equivalent to the square root. Therefore, $(-3)^{0.5}$ is the same as the square root of $-3$ .
Evaluate square root: Evaluate the square root of a negative number. $\newline$ The square root of a negative number is not a real number; it is an imaginary number. Therefore, the square root of $-3$ is an imaginary number.
Write final answer: Write the final answer using the imaginary unit $i$ . The square root of $-3$ can be written as $\sqrt{3} \cdot i$ , where $i$ is the imaginary unit. Final Answer: $\sqrt{3} \cdot i$