Question

Evaluate 16 1/2 x 2⁻³. Give your answer as a fraction in its simplest form.

Answer 1

The result of
`\(16 (1)/(2) * 2^(-3)\)` is
`\((1)/(4)\).`

Explanation:

To evaluate
`\(16 (1)/(2) * 2^(-3)\),` let's break it down step by step. First, convert the mixed number to an improper fraction:

`\[16 (1)/(2) = ((16 * 2) + 1)/(2) = (32 + 1)/(2) = (33)/(2).\]`

Now, rewrite the expression with the improper fraction:

`\[(33)/(2) * 2^(-3).\]`

To multiply, combine the numerators and denominators:

`\[(33 * 1)/(2 * 2^3) = (33)/(8).\]`

Now, simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:

`\[(33)/(8) / 1 = (33)/(8).\]`

However, the fraction \(\frac{33}{8}\) is not in its simplest form. To simplify further, note that both 33 and 8 share a common factor of 1. Divide both the numerator and denominator by 1:

`\[(33 / 1)/(8 / 1) = (33)/(8).\]`

So, the final simplified answer is
`\((33)/(8)\).`

Answer 2

The evaluated expression 16 1/2 x 2⁻³ simplifies to 2⁵ or 32.

Step-by-step explanation:

The expression 16 1/2 x 2⁻³ can be broken down into two parts: the whole number 16 and the fraction 1/2, multiplied by 2 raised to the power of -3.

Firstly, let's evaluate the whole number part:

16 x 1 = 16.

Now, let's focus on the fraction part:

1/2 x 2⁻³.

To simplify the fraction, we use the rule that aⁿ ÷ aᵐ = aⁿ⁻ᵐ. Therefore, 2⁻³ in the denominator can be rewritten as 1/2³ in the numerator:

1/2 x 1/2³.

Now, combine the fractions by multiplying the numerators and denominators separately:

(1 x 1) / (2 x 2³) = 1/16.

Now, combine the whole number and fraction parts:

16 + 1/16 = 16.1/16.

Finally, simplify the mixed number to the whole number 32:

16.{1/16} = 2⁵ = 32.

In summary, the expression 16 1/2 x 2⁻³ simplifies to 32.