10^{-1} / 8^{-2} =
A) 0.125
B) 1.25
C) 1
D) 10
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To solve the expression ( frac{10^{-1}}{8^{-2}} ), we will simplify it step by step.
1. Convert the negative exponents:
– ( 10^{-1} = frac{1}{10} )
– ( 8^{-2} = frac{1}{8^2} = frac{1}{64} )
2. Rewrite the fraction:
– The expression becomes ( frac{frac{1}{10}}{frac{1}{64}} ).
3. Divide the fractions:
– Dividing by a fraction is the same as multiplying by its reciprocal, so:
[
frac{1}{10} times 64 = frac{64}{10} = 6.4
]
4. Simplifying further:
– Another way to look at ( frac{10^{-1}}{8^{-2}} ) is ( 10^{-1} times 8^2 = 10^{-1} times 64 ), which is also ( frac{64}{10} ).
Since the answer is ( 6.4 ), which is not among the given options. Let’s double check the available answers.
If we take the original expression to the decimal computation:
– ( 10^{-1} = 0.1 )
– ( 8^{-
To solve ( 10^{-1} / 8^{-2} ), we can rewrite it using positive exponents:
1. Rewrite the expression:
[
10^{-1} = frac{1}{10} quad text{and} quad 8^{-2} = frac{1}{8^2} = frac{1}{64}
]
2. Now substituting back into the equation:
[
frac{frac{1}{10}}{frac{1}{64}} = frac{1}{10} times 64 = frac{64}{10} = 6.4
]
None of the answers match, but if we consider the exponent steps:
1. ( 10^{-1} = 0.1 )
2. ( 8^{-2} = frac{1}{64} approx 0.015625 )
So, dividing these gives ( frac{0.1}{0.015625} approx 6.4 ).
However, using another method gives:
[
frac{10^{-1}}{8^{-2}} = 10^{-1} times 8^{2} = 10^{-1} times 64
]
Calculating ( 64 div 10 = 6.4 ).
The closest valid answer could include misinterpretation, so please verify the workings