Question

Find X (5/3)^-2 x (5/3)^-14=(5/3) ^8x

Answer 1

x = -2

Step-by-step explanation:

Given:

${(\dfrac{5}{3})}^{ - 2} \times {\dfrac{5}{3}}^{ - 14} = {(\dfrac{5}{3})}^{8x}$

To find:

The value of x

Solution:

Just use the laws of Indices and you will get the

answer..... :)

${(\dfrac{5}{3})}^{ - 2} \times {\dfrac{5}{3}}^{ - 14} = {(\dfrac{5}{3})}^{8x} \\ \\ {(\dfrac{5}{3})}^{ (- 2 - 14)} = {(\dfrac{5}{3})}^{ 8x} \\ \\ {(\dfrac{5}{3})}^{ - 16} = {(\dfrac{5}{3})}^{8x} \\ \\ [\text{Eliminating the base from both side}] \\ \\ - \cancel{16} = \cancel{8 \: }x \\ \\ x = - 2$

Therefore, the required value of x is -2

${\underline{{\text{Laws of Indices}}}}$

${a}^{n}.{a}^{m}={a}^{(n + m)}$

${a}^{-1}=\dfrac{1}{a}$

$\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}$

${({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}$

${a}^{\frac{1}{x}}=\sqrt[x]{a}$

[tex]

[Where all variables are real and greater than 0]