Question

Find the value of x so that: .a.(5/3)power-2 , ×(5/3) power-14,=(5/3)power8x
b.(-2)power3×(-2)power-6=(-2)power2x-1​

Answer 1

Answer:

a. x=-2 b. x= 5

Step-by-step explanation:

a. LHS

=(5/3)^-2 x (5/3)^-14

= (5/3)^-16. {since, by property, a^m x a^n = a^(m+n)}

RHS

=(5/3)^8x

LHS=RHS , Implies that (5/3)^-16 = (5/3)^8x

-16 =8x

therefore x=-16/8=-2

b.Similarly by above property,

LHS

(-2)^3 x (-2)^6 = (-2)^(3+6)= (-2)^9

and LHS=RHS

therefore, (-2)^9=(-2)^2x-1

comparing the powers, we get,

9=2x-1

x=(9+1)/2=10/2=5.