Answer:
[tex]\Large \text{$ \frac{1}{w^2} $}[/tex]
Step-by-step explanation:
Given the exponential expression, [tex]\displaytext\mathsf{w^3\:\times\:w^{-5}}[/tex], where it involves the multiplication of the same base, w, with varying powers.
Using the Product Rule of Exponents, where it states that, [tex]\displaystyle\mathsf{a^{m}\:\times\:a^{n}\:=\:a^{(m\:+\:n)}}[/tex].
Hence, we simply need to add the exponents:
[tex]\displaytext\mathsf{w^3\:\times\:w^{-5}\:=\:w\:^{[3\:+\:(-5)]}\:=\:w^{-2}}[/tex]
Next, apply the Negative Exponent Rule, where it states that: [tex]\displaystyle\mathsf{a^{-n}\:=\:\frac{1}{a^n}}[/tex].
Transforming the negative exponent of [tex]\displaytext\mathsf{w^{-2}}[/tex] becomes a positive exponent by using the Negative Exponent Rule.
[tex]\displaytext\mathsf{w^{-2}\:=\:\frac{1}{w^2}}[/tex]
