Question

if x is a positive integer such than x^9=r and x^5=w, which of the following must be equal to x^13?

A. rw-1
B. r+w-1
C. r²/w
D. r²-w

Answer 1

${\large{\bold{Given:}}}$

• x⁹ = r ___(1)
• x⁵ = w ___(2)

${\large{\bold{To \ Find:}}}$

• What is the value of x¹³ ?

${\large{\bold{Solution:}}}$

If we square the equation (1) we get,

${\Rightarrow{\small{\tt{ (x^9 = r)^2 }}}}$

${\Rightarrow{\small{\tt{ x^{18 }= r^2 \dots \dots \: eq {}^{n} \: (3) }}}}$

If we divide equation Equation(3) by (2) we get

${\hookrightarrow{\small{\tt{ \dfrac{x^{18}}{x^5} = \dfrac{r^2}{w}}}}}$

${\hookrightarrow{\small{\tt{x^{13} = \dfrac{r^2}{w}}}}}$

So, option(c) is correct