To simplify the expression [tex]\(\frac{4}{y^{-3}}\)[/tex], let's break it down step-by-step:
1. Understand the properties of exponents:
- Specifically, recall that a negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. This means that [tex]\(y^{-3} = \frac{1}{y^3}\)[/tex].
2. Substitute [tex]\(y^{-3}\)[/tex] with [tex]\(\frac{1}{y^3}\)[/tex] in the given expression:
[tex]\[
\frac{4}{y^{-3}} = \frac{4}{\frac{1}{y^3}}
\][/tex]
3. Simplify the complex fraction:
- Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore,
[tex]\[
\frac{4}{\frac{1}{y^3}} = 4 \times y^3
\][/tex]
Thus, the correct simplification of the expression [tex]\(\frac{4}{y^{-3}}\)[/tex] is [tex]\(4y^3\)[/tex].
Among the given options:
1. [tex]\(4y^3\)[/tex]
2. [tex]\(\frac{4}{y^3}\)[/tex]
3. [tex]\(\frac{y^3}{4}\)[/tex]
4. This expression is already simplified
The correct answer is:
[tex]\[4y^3\][/tex]
