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Fraction multiplication is a core concept in prealgebra. It involves multiplying the numerators (top numbers) together and the denominators (bottom numbers) together. For example, if we want to multiply \( \frac{1}{8} \) by \( \frac{1}{25} \), we multiply the numerators: 1 × 1 = 1, and then the denominators: 8 × 25 = 200. Therefore, \( \frac{1}{8} \times \frac{1}{25} = \frac{1}{200} \).
Fraction multiplication can be simplified if any of the numerators or denominators share common factors, but in this case, since both are prime numbers, the resulting fraction remains in its simplest form.
Understanding how to multiply fractions by multiplying across is essential for tackling more complex algebraic equations.

Exponents represent repeated multiplication of a number by itself. In this exercise, we deal with the exponent \( \frac{1}{5}^2 \). This means \( \frac{1}{5} \) multiplied by \( \frac{1}{5} \), or \( \frac{1}{5} \times \frac{1}{5} \).
When multiplying fractions with exponents, always remember to multiply the numerators and denominators separately. So, \( \frac{1}{5} \times \frac{1}{5} = \frac{1 \times 1}{5 \times 5} = \frac{1}{25} \).
Exponents are vital for simplifying expressions because they reduce the need for repetitive multiplication, making it easier to handle large numbers or fractions.

A common denominator is necessary for adding or subtracting fractions. It’s the least common multiple (LCM) of the denominators of the fractions involved.
In our exercise, we need to add \( 6.5 \) and \( \frac{1}{200} \). First, convert \( 6.5 \) to a fraction, which is \( \frac{13}{2} \). To add \( \frac{13}{2} \) and \( \frac{1}{200} \), we find a common denominator: the LCM of 2 and 200 is 200. Convert \( \frac{13}{2} \) to have the denominator 200: \( \frac{13}{2} = \frac{1300}{200} \).
Now, add \( \frac{1300}{200} \) and \( \frac{1}{200} \): \( \frac{1300}{200} + \frac{1}{200} = \frac{1301}{200} \).
Using a common denominator allows us to add the fractions seamlessly and arrive at the correct result.