If $x$ be any integer different from zero and $m$ be any positive integer, then $x^{- m}$ is equal to:

$x^{m}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$- x^{m}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{1}{x^{m}}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$- \frac{1}{x^{m}}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$\frac{1}{x^{m}}$

Explanation for correct option:
Find the value of the given exponent
By the laws of indices, For any non-zero integer $a$ ,
$a^{- m} = \frac{1}{a^{m}}$
i.e., when the power is negative on a number, then the result is the reciprocal of the given number raised to the same power with a positive sign.
$∴ x^{- m} = \frac{1}{x^{m}}$
For example, $13^{- 5} = \frac{1}{13^{5}}$
Hence, option(C) is the correct answer.

Suggest Corrections

Similar questions

Use Euclid’s division lemma to show that the square of any positive integer is either of form 3m or 3m + 1 for some integer m.

[Hint: Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.]

Q. In each of the following state if the statement is true (T) or false (F):
(i) The quotient of two integers is always an integer.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.
(iv) Every fraction is a rational number.
(v) Every rational number is a fraction
(vi) If

\frac{a}{b}

is a rational number and m any integer, then

\frac{a}{b} = \frac{a \times m}{b \times m}

(vii) Two rational numbers with different numerators cannot be equal.
(viii) 8 can be written as a rational number with any integer as denominator.
(ix) 8 can be written as a rational number with any integer as numerator.
(x)

\frac{2}{3} is equal to \frac{4}{6} .

Question 12

In the following question, out of the four options, only one is correct. Write the correct answer:

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

Q. If '

x

' be any non-zero integer, then

x^{0}

is equal to:

Show that square of any positive integer cannot be of the form 6m+2 or 6m+5 for any integer m

Join BYJU'S Learning Program

If x be any integer different from zero and m be any positive integer, then x-m is equal to:

If $x$ be any integer different from zero and $m$ be any positive integer, then $x^{- m}$ is equal to: