Test Index

Indices

© examsnet.com

Question : 34 of 86

Marks: +1, -0

If

m=x^{a}, n=x^{b}, p=x^{c}

m^{b-c} n^{c-a} p^{a-b}

equals;

0
1
$-1$
2 .

Solution:

Concept:

Substitute the given expressions and simplify the exponent using algebraic expansion.

Explanation:

Given

m = x^a

,

n = x^b

,

p = x^c

.

Then

m^{b-c} = (x^a)^{b-c} = x^{a(b-c)}

.

Similarly,

n^{c-a} = x^{b(c-a)}

and

p^{a-b} = x^{c(a-b)}

.

Multiplying:

x^{a(b-c)} \cdot x^{b(c-a)} \cdot x^{c(a-b)} = x^{a(b-c) + b(c-a) + c(a-b)}

.

Simplify exponent:

a(b-c) + b(c-a) + c(a-b) = ab - ac + bc - ab + ac - bc = 0

.

Thus expression equals

x^0 = 1

.

Answer:

1

© examsnet.com

Go to Question:

Prev Question

Next Question