Question

The expression
`( x ^3)(x^( - 17) )`is equivalent to
`x ^(n)`What is the value of n?

Answer 1

Answer : n = -14

`\begin{gathered} (x^3)(x^(-17))=x^n \\ \text{This can be written as } \\ x^3\cdot x^(-17)=x^n \\ \text{According to the first law of indicies} \\ x^a\cdot x^b=x^{a\text{ + b}} \\ \text{let a = 3, and b = -17} \\ x^3\cdot x^{-17\text{ }}=x^{3\text{ + (-17)}} \\ =x^{3\text{ - 17}} \\ =x^(-14) \\ \text{ Since, x}^{-14\text{ }}=x^n \\ \text{Therefore, n = -}14 \\ n\text{ = -}14 \end{gathered}`