Chapter 5 Polynomials and Polynomial Functions - 5.1 Use Properties of Exponents - 5.1 Exercises - Skill Practice - Page 334: 45

$a^{-4}b^9$

Here, we have $(a^5 b^4)^2=(a^5)^2 (b^4)^2$ Here, we have $(a^5)^2 = a^{10}$ and $(b^4)^2=b^8$ Now, $a^{10}b^{8}=a^{14} b^{-1}=e$ This gives; $e=\dfrac{a^{10}b^{8}}{a^{14} b^{-1}}=a^{10-14} b^{8-(-1)}$ Hence, $e=a^{-4}b^9$