Question
Evaluate the following. Click on "Not a real number" if applicable. (a) \( -343^{\frac{1}{3}}=-7 \) (b) \( -64^{\frac{1}{2}} \) Not a real number
Ask by Hills Thornton. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
(a) \( -343^{\frac{1}{3}} = -7 \)
(b) \( -64^{\frac{1}{2}} = -8 \)
Solution
Calculate or simplify the expression \( -343^{\frac{1}{3}} \).
Calculate the value by following steps:
- step0: Calculate:
\(-343^{\frac{1}{3}}\)
- step1: Evaluate the power:
\(-7\)
Calculate or simplify the expression \( -64^{\frac{1}{2}} \).
Calculate the value by following steps:
- step0: Calculate:
\(-64^{\frac{1}{2}}\)
- step1: Evaluate the power:
\(-8\)
(a) \( -343^{\frac{1}{3}} = -7 \)
(b) \( -64^{\frac{1}{2}} = -8 \)
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Simplify this solution Beyond the Answer
The expressions can be evaluated as follows: (a) \( -343^{\frac{1}{3}}= -7 \): This statement is true! The cube root of -343 is -7, since \((-7) \times (-7) \times (-7) = -343\). So, yay for negative cubes! (b) \( -64^{\frac{1}{2}} \): You would click on "Not a real number" for this one. The square root of -64 does not produce a real number; rather, it ventures into the realm of imaginary numbers! Specifically, it equals \(8i\), where \(i\) is the imaginary unit. Hence, real number fans, beware!
