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How do you simplify #256^(-7/8)#?

Answer 1

Savannah Anderson

#color(red)(256^(-7/8)#

#= ((256)^(1/8))^-7#

# = (root(8)256) ^ -7#

# = (2)^-7#

# = 1/(2^7)#

#color(green)( = 1/ 128#

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Answer 2

Genesis Allen

To simplify ( 256^{-\frac{7}{8}} ), first recognize that ( 256 = 2^8 ). Then, apply the properties of exponents:

[ 256^{-\frac{7}{8}} = (2^8)^{-\frac{7}{8}} = 2^{-\frac{7}{8} \times 8} = 2^{-7} ]

So, ( 256^{-\frac{7}{8}} ) simplifies to ( 2^{-7} ).

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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.

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