Question

- Hair grows at a rate of 1/64 inch per day. Write this number using negative exponents.

Answer 1

`4^(-3)`

Explanation:

`4^(3)` = 64

Take the reciprocal of both sides.

1/64 =
`4^{-3`

Answer 2

Hair grows at a rate of
`\(2^(-6)\)` inches per day.

The rate of hair growth, 1/64 inch per day, can be expressed using negative exponents to denote a fraction as a decimal.

The denominator of the fraction, 64, can be expressed as
`\(2^6\)` because
`\(2^6 = 64\)`.

Writing the rate of growth with a negative exponent involves inverting the fraction and changing the sign of the exponent. For instance,
`\(1/64\)` can be rewritten as
`\(2^(-6)\)` because when the denominator is inverted, it becomes
`\(2^6\)` in the denominator, and the negative sign indicates the reciprocal.

Therefore, the rate of hair growth, 1/64 inch per day, in terms of negative exponents, is
`\(2^(-6)\)` inches per day. This implies that each day, hair grows at a rate of
`\(2^(-6)\)` inches.

Negative exponents represent fractions in their reciprocal form. In this context,
`\(2^(-6)\)` signifies that the growth rate is one sixty-fourth (1/64) of an inch, with the negative exponent indicating the reciprocal, meaning it's the same as
`\(1/2^6\)` or
`\(1/2^6\)` inches per day. This notation provides a way to represent small quantities, such as the hair growth rate, using negative exponents in a concise and clear manner.