Question

find the value of x
(2/7)-3×(2/7)^-11=(2/7)^7x​

Answer 1

Step-by-step explanation:

Given that:-

Given that:-(2/7)^-3×(2/7)^-11=(2/7)^7x

we know that a^m×a^n=a^(m+n)

=>(2/7)^{(-3)+(-11)}=(2/7)^7x

=>(2/7)^-14=(2/7)^7x

since bases are equal then exponents must be equal.

=>-14=7x

=>7x=-14

=>x=-14/7

=>x=-2

The value of x=-2

check:-

LHS:-

(2/7)^-3×(2/7)^-11

=>(2/7)^-14

RHS:-

(2/7)^7x

=>(2/7)^7×-2

=>(2/7)^-14

LHS =RHS is true for the value of x=-2

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

$\sf {\bigg(\dfrac{2}{7}\bigg) }^{ - 3} \times { \bigg(\dfrac{2}{7}\bigg)}^{ - 11} = { \bigg(\dfrac{2}{7}\bigg)}^{7x}$

Concept:

• When two values or variable gets multiply with each other having same base with different powers then their power gets added during multiplication.
• In the same manner if two values of same base with unlike powers when divides then their power gets subtracted.

$\sf= > { \dfrac{2}{7} }^{ - 3 + ( - 11)} = {\bigg (\dfrac{2}{7}\bigg)}^{7x}$

$\sf= > {\bigg( \dfrac{2}{7}\bigg) }^{ - 3 - 11} = {\bigg (\dfrac{2}{7} \bigg)}^{7x}$

=>Here,we see that on both side same value so it gets automatically cancelled.

$\sf= > - 14 = 7x$

$\sf= > x = - 2$

$\therefore$$\bold{x=\:-2}$