How do you evaluate #(16^{\frac{1}{2}})^3#?

Answer 1

You would multiply the exponents.

Because of the power of a power property, you would multiply #1/2# and 3, giving you #3/2#. Now, you have #16^(2/3)# or the cube root of #16^2#. This equals to about 6.3496 if you plug it into a calculator. Hope this helps!

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Answer 2

Savannah Anderson

To evaluate ((16^{\frac{1}{2}})^3):

Simplify the exponent ( \frac{1}{2} ) by taking the square root of 16: ( \sqrt{16} = 4 ).
Substitute the result back into the expression: ( 4^3 ).
Cube the base: ( 4 \times 4 \times 4 = 64 ).
The value of ( (16^{\frac{1}{2}})^3 ) is ( 64 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.