If x be any non-zero integer and m, n be negative integers, then x^m × xⁿ is equal to
(a) x^m
(b) x^{m + n}
(c) xⁿ
(d) x^{m - n}

Solution:

The correct option is (b)

By laws of indices we have a^m × aⁿ = a^{m + n}, irrespective of power is positive integer or negative integer

✦ Try This: The result x^{m + n} = x^m × xⁿ is not applicable in

(a) When x is negative integer m and n are positive integer

(b) When x is positive integer and m and n are negative integers

(c) When x is any integer and x ≠ 0, m and n are any integer

(d) When x = 0, m and n are also zero

The correct option is (d)

By the definition of the laws of exponent it is clear that these laws are not applicable when both base as well the index are zero.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 12

If x be any non-zero integer and m, n be negative integers, then x^m × x^m is equal to (a) x^m, (b) x^{m + n}, (c) xⁿ, (d) x^{m - n}

Summary:

If x be any non-zero integer and m, n be negative integers, then x^m × x^m = x^{m + n}

☛ Related Questions:

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