Question

Find the value of x it's simple easy​

Answer 1

Step-by-step explanation:

Given :-

(-2/3)^-13 × (3/-2)^8 = (-2/3)^(-2x+1)

To find :-

Find the value of x ?

Solution :-

Given equation is

(-2/3)^-13 × (3/-2)^8 = (-2/3)^(-2x+1)

We know that a^-n = 1/a^n

(-2/3)^-13 = 1/(-2/3)^13 = (-3/2)^13

Above equation becomes

=> (-3/2)^13 × (-3/2)^8 = (-2/3)^(-2x+1)

=> (-3/2)^(13+8) = (-2/3)^(-2x+1)

Since a^m × a^n = a^(m+n)

=> (-3/2)^21 = (-2/3)^(-2x+1)

=> (-2/3)^-21 = (-2/3)^(-2x+1)

Since a^-n = 1/a^n

=> -21 = -2x+1

Since the bases are equal then exponents must be equal.

=> -2x+1 = -21

=> -2x = -21-1

=> -2x = -22

=> x = -22/-2

=> x = 11

Therefore, x = 11

Answer:-

The value of x for the given problem is 11

Check:-

LHS of the given equation is

(-2/3)^-13 × (3/-2)^8

=> (-2/3)^-13 × (-2/3)^-8

Since a^-n = 1/a^n

=> (-2/3)^(-13-8)

=> (-2/3)^-21----------(1)

If x = 11 then RHS of the given equation is

(-2/3)^(-2×11+1)

=> (-2/3)^(-22+1)

=> (-2/3)^-21-----------(2)

From (1)&(2)

LHS = RHS is true for x = 11

Verified the given relations in the given problem.

Used formulae:-

• a^-n = 1/a^n
• a^m × a^n = a^(m+n)
• If the bases are equal then exponents must be equal.