# Prove that : X^(A(B - C))/X^B(A - C) ÷ ((X^B)/(X^A))^C = 1 - Mathematics

Sum

Prove that :
[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1

#### Solution

We need to prove that
[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1

LHS =

= x^[a(b - c ) - b( a - c )] ÷ x^(bc)/x^(ac)

= x^( ab - ac - ab + bc ) ÷ x^( bc - ac )

= x^( ab - ac - ab + bc - bc + ac )
= x^0
= 1
= RHS

Concept: Solving Exponential Equations
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#### APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 7.2 | Page 100