To determine which expression is equivalent to [tex]\( 5 y^{-3} \)[/tex], we need to perform a series of algebraic manipulations. Let's break it down step-by-step.
1. Understanding Negative Exponents:
The expression [tex]\( y^{-3} \)[/tex] can be rewritten using the property of negative exponents, which states that:
[tex]\[
y^{-n} = \frac{1}{y^n}
\][/tex]
2. Applying the Negative Exponent Property:
Applying this property to [tex]\( y^{-3} \)[/tex], we get:
[tex]\[
y^{-3} = \frac{1}{y^3}
\][/tex]
3. Multiplying by 5:
Now, multiply the result by 5, as in the original expression [tex]\( 5 y^{-3} \)[/tex]:
[tex]\[
5 y^{-3} = 5 \cdot \frac{1}{y^3}
\][/tex]
4. Simplifying the Expression:
Simplifying the multiplication, we have:
[tex]\[
5 \cdot \frac{1}{y^3} = \frac{5}{y^3}
\][/tex]
Thus, the expression equivalent to [tex]\( 5 y^{-3} \)[/tex] is:
[tex]\[
\frac{5}{y^3}
\][/tex]
Therefore, the correct expression from the given choices is:
[tex]\[
\boxed{\frac{5}{y^3}}
\][/tex]
