If x be any integer different from zero and m- n be any integers- then -x-m -n is equal to- -a- x-m-n -b- x-mn -c- x-m-n -d- x-m-n - Maths Q-A

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Standard V

Mathematics

Evaluating the Given Number

If x be any i...

Question

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

$x^{m + n}$

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$x^{m n}$

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

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$x^{m - n}$

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Solution

The correct option is B
$x^{m n}$

Explanation for correct option:
Find the value of the given exponent
By the law of exponents,
${(z^{m})}^{n} = z^{m n}$
where $m, n$ can be both integer as well as non-integer number.
Thus, we need to multiply the powers of the number to get the result.
${∴ (x^{m})}^{n} = x^{m n}$
For example, ${(13^{2})}^{6} = 13^{2 \times 6} = 13^{12}$
Hence, option(B), $x^{m n}$ is the correct answer.

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Similar questions

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:

Q. If

a

is a non-zero integer and

m

and

n

are any integers, then

a^{m} \times a^{n}

= .

If $a$ is any non-zero integer and $m, n$ are two whole numbers, then $a^{m} \times a^{n} =______.$

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If x be any integer different from zero and m,n be any integer, then (xm)n is equal to:

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