Question

See attached pic. Simplify the expression using only positive exponents in the result. Parts A-D

Answer 1

Simplify the expression using only positive exponents in the result:

(a)

`\begin{gathered} ((16x^4y^3)/(4x^7y))^5 \\ (\frac{16^{}}{4^{}})^5.(x^(4*5))/(x^(7*5))\text{.}(y^(3*5))/(y^5) \\ 4^5.(x^(20))/(x^(35)).(y^(15))/(y^5) \\ 1024.x^(20-35).y^(15-5) \\ 1024x^(-15)y^(10) \\ (1024y^(10))/(x^(15)) \end{gathered}`

(b)

`\begin{gathered} (p^(-4)(p^(-2))^(-5))/(p^2) \\ (p^(-4).p^(-2)^(*-5))/(p^2) \\ (p^(-4).p^(10))/(p^2) \\ =p^(-4+10).p^(-2) \\ =p^(6-2) \\ =p^4 \end{gathered}`

(c)

`\begin{gathered} (3ab^3)(-5b^2c^4)(a^2c) \\ 3.(-5)a\mathrm{}a^2.\text{b}^3\text{.b}^2\text{.c}^4\text{.c} \\ -15a^(1+2).b^(3+2).c^(4+1) \\ -15a^3b^5c^5 \end{gathered}`

(d)

`\begin{gathered} ((5x^(-1)y^3)/(10x^2y^5))^(-2) \\ =((5)/(10).x^(-1).x^(-2).y^3.y^(-5))^(-2) \\ =((1)/(2).x^(-1-2).y^(3-5))^(-2) \\ =((1)/(2)x^(-3)y^(-2))^(-2) \\ =(1)/(4)x^(-3(-2))y^(-2(-2)) \\ =(1)/(4)x^6y^4 \end{gathered}`