Question

Part A: Use the properties of exponents to explain why -18 raised to the power of 1 over 5- is called the fifth root of 18. (5 points)

Part B: The length of a rectangle is 2 units and its width is -square root of 2- unit. Is the area of the rectangle rational or irrational? Justify your answer. (5 points)

Answer 1

@gottennis121 @steffie84

Answer 2

I do part A for you.

If 18 ^(1/5) is the fifth root.

then -18^(1/5) multiplied by itself 5 times must equal the base value

\[-18^{\frac{ 1 }{ 5 }}*-18^{\frac{ 1 }{ 5 }}*-18^{\frac{ 1 }{ 5 }}*-18^{\frac{ 1 }{ 5}}*-18^{\frac{ 1 }{5 }}=\]
\[-18^{(\frac{ 1 }{ 5 }+\frac{ 1 }{ 5}+\frac{ 1 }{ 5 }+\frac{ 1 }{ 5 }+\frac{ 1 }{ 5 })}=-18^{1}\]

Since -18^1 equals the base value -18, then -18^(1/5) is the fifth root.