Let's simplify the expression [tex]\(\left(\frac{1}{x}\right)^{-3}\)[/tex].
1. Understand Negative Exponents:
The negative exponent rule states that [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex]. Applying this property, we can rewrite anything raised to a negative exponent as the reciprocal of the base raised to the corresponding positive exponent.
2. Rewrite the Expression:
Initially, we have [tex]\(\left(\frac{1}{x}\right)^{-3}\)[/tex].
3. Simplify the Negative Exponent:
Apply the negative exponent rule:
[tex]\[
\left(\frac{1}{x}\right)^{-3} = \left(\frac{1}{\left(\frac{1}{x}\right)^3}\right) = x^3
\][/tex]
So, the simplified expression is [tex]\(x^3\)[/tex]. Hence, in terms of the base [tex]\(x\)[/tex], it will be written as:
[tex]\[ x^{3} \][/tex]
Therefore, the expression [tex]\(\left(\frac{1}{x}\right)^{-3}\)[/tex] simplifies to [tex]\(x^3\)[/tex].
