Question

Move the expressions into the columns to show which expressions are equivalent to the value given at the top of each column. Not all expressions will be used


1/8 - 8


options: 2superscript2, 2superscript4/2-superscript7, 2-superscript3, 2superscript8/2superscript5, 2superscript0/2-superscript3, 1/2superscript7.2-superscript4

Answer 1

To determine which expressions are equivalent to \( \frac{1}{8} - 8 \), we first need to simplify \( \frac{1}{8} - 8 \).

1. Convert \( 8 \) into a fraction with a denominator of 8:
\[
8 = \frac{8}{1} = \frac{8 \cdot 8}{8} = \frac{64}{8}
\]

2. Now, combine the two fractions:
\[
\frac{1}{8} - 8 = \frac{1}{8} - \frac{64}{8} = \frac{1 - 64}{8} = \frac{-63}{8}
\]

Now let's evaluate the given options to see which ones are equivalent to \( -\frac{63}{8} \):

1. \( 2^2 = 4 \)
2. \( \frac{2^4}{2^7} = \frac{16}{128} = \frac{1}{8} \)
3. \( 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \)
4. \( \frac{2^8}{2^5} = \frac{256}{32} = 8 \)
5. \( \frac{2^0}{2^{-3}} = \frac{1}{\frac{1}{8}} = 8 \)
6. \( \frac{1}{2^7} \cdot 2^{-4} = \frac{1}{128} \cdot \frac{1}{16} = \frac{1}{2048} \) (not equivalent)

None of these expressions yield a value equivalent to \( -\frac{63}{8} \).

As such, it appears that no expressions provided are equivalent to \( \frac{1}{8} - 8 \).