Question

Express each of the following rational numbers in power notation
(i) -1/125

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Answer 1

`\displaystyle \large{-5^(-3)}`

Explanation:

Given:

`\displaystyle \large{-(1)/(125)}`

Convert to exponent using the laws of exponent:

`\displaystyle \large{(1)/(a^n) = a^(-n)}`

That means we must find the base and exponent for 125, which is
`\displaystyle \large{5^3}`:

`\displaystyle \large{-(1)/(125) = -(1)/(5^3)}`

From the law of exponent:

`\displaystyle \large{-(1)/(5^3) = -5^(-3)}`

Therefore, the solution is
`\displaystyle \large{-5^(-3)}`