Question

Simplify a ^-4 / 4a^6

Answer 1

The simplified expression for
`\( (a^(-4))/(4a^6) \) is \( (1)/(4a^(10)) \)`.

Let's start from the beginning and simplify
`\((a^(-4))/(4a^6)\)`:

1. Apply the quotient rule for exponents:
`\(a^(-4)/4a^6\)`.

2. Subtract the exponent in the denominator from the exponent in the numerator:
`\(a^(-4-6) = a^(-10)\)`.

3. Express the result as the reciprocal of
`\(a^(10)\): \((1)/(a^(10))\)`.

4. To represent it more conventionally, multiply both the numerator and denominator by 4:
`\((1)/(4a^(10))\)`.

Therefore, the correct and simplified expression is
`\((1)/(4a^(10))\)`, as the reciprocal of
`\(4a^(10)\)`.