10^{-1} / 8^{-2} =

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