Using the Power of a Product Rule

Use the product and quotient rules and the new definitions to simplify each expression.

1. ⓐ ${\left(a{b}^2\right)}^3={\left(a\right)}^3\cdot {\left(b^2\right)}^3=a^{1\cdot 3}\cdot b^{2\cdot 3}=a^3{b}^6$
2. ⓑ ${\left(2t\right)}^{15}={\left(2\right)}^{15}\cdot {\left(t\right)}^{15}=2^{15}{t}^{15}=32,768t^{15}$
3. ⓒ ${\left(\mathrm{-2}{w}^3\right)}^3={\left(\mathrm{-2}\right)}^3\cdot {\left(w^3\right)}^3=\mathrm{-8}\cdot w^{3\cdot 3}=\mathrm{-8}{w}^9$
4. ⓓ $\frac{1}{{\left(\mathrm{-7}z\right)}^4}=\frac{1}{{\left(\mathrm{-7}\right)}^4\cdot {\left(z\right)}^4}=\frac{1}{2,401z^4}$
5. ⓔ ${\left(e^{\mathrm{-2}}{f}^2\right)}^7={\left(e^{\mathrm{-2}}\right)}^7\cdot {\left(f^2\right)}^7=e^{\mathrm{-2}\cdot 7}\cdot f^{2\cdot 7}=e^{\mathrm{-14}}{f}^{14}=\frac{f^{14}}{e^{14}}$