Question

1. What would you do with each problem in order to get it in its simplest properform? Use words to explain the specific details to why you used thatprocess/rule.Number 1: a-d

Answer 1

Given the indicial expressions, we can find their solution below.

Explanation

Part A: Divison

$\frac{x^9}{x^7}$

If the two terms have the same base (in this case x) and are to be divided their indices are subtracted.

$\begin{gathered} In\text{ }general:\dfrac{x^m}{x^n}=x^{m-n} \\ Hence,\frac{x^9}{x^7}=x^{9-7}=x^2 \end{gathered}$

Answer:

$x^2$

Part b: Brackets

$(x^7)^9$

If a term with a power is itself raised to a power then the powers are multiplied together.

$\begin{gathered} In\text{ }general:(x^m)^n=x^{m\times n} \\ Hence(x^7)^9=x^{7\times9}=x^{63} \end{gathered}$

Answer:

$x^{63}$

Part C: Negative powers

$(x)^{-9}$

A negative power can be written as a fraction.

$\begin{gathered} In\text{ }general:x^{-m}=\dfrac{1}{x^m} \\ Hence,\text{ x}^{-9}=\frac{1}{x^9} \end{gathered}$

Answer:

$\frac{1}{x^9}$

Part D: Multiplication

$x^7\times x^9$

If the two terms have the same base (in this case x) and are to be multiplied together their indices are added.

$In\text{ }general:x^m\times x^n=x^{m+n}$

Answer:

$x^7\times x^9=x^{7+9}=x^{16}$

Answer:

$x^{16}$