A-n-b-n- -a-b-na-b-na-n-b-a-b-n

The correct option is A (a/b)^nFor any non zero integers a and b, a^n/b^n=(a/b)^n, where 'n' is any integer. For example, 2^ 2/ 3^ 2=( 2/3)^ 2 ...

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Byju's Answer

Standard VIII

Mathematics

Dividing Terms with the Same Exponent

a^n/b^n= ____...

Question

$\frac{a^{n}}{b^{n}} =$ _____

(\frac{a}{b})^{n}

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(\frac{a}{b})^{- n}

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\frac{a}{b^{n}}

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\frac{a^{n}}{b}

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Solution

The correct option is A $(\frac{a}{b})^{n}$
For any non-zero integers a and b,
$\frac{a^{n}}{b^{n}} = (\frac{a}{b})^{n}$ ,
where 'n' is any integer.
For example,
$\frac{2^{- 2}}{- 3^{- 2}} = (- \frac{2}{3})^{- 2}$

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Similar questions

Q. If

A

and

B

are square matrices of the same order such that

A B = B A

, then prove by induction that

{A B}^{n} = B^{n} A

. Further, prove that

{(A B)}^{n} = A^{n} B^{n}

for all

n \in N

If A and B are square matrices of the same order such that AB = BA, then prove by induction that. Further, prove that for all n ∈ N

Q. If

\frac{a^{n + 1} + b^{n + 1}}{a^{n} + b^{n}}

is the A.M. of a and b, then n = ___________.

Q. Let

A

and

B

be two matrices different from

I

such that

A B = B A

and

A^{n} - B^{n}

is invertible for some positive integer

n

. If

A^{n} - B^{n} = A^{n + 1} - B^{n + 1} = A^{n + 2} - B^{n + 2}

, then

Q. Let

A

and

B

be two matrices different from

I

such that

A B = B A

and

A^{n} - B^{n}

is invertible for some natural number

n

. If

A^{n} - B^{n} = A^{n} + 1 - B^{n} + 1 = A^{n + 2} - B^{n + 2}

, then
I.

(I - A)

is singular
II.

(I - B)

is singular
III.

A + B = A B + I

IV.

(I - A) (I - B)

is non-singular

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anbn= _____

The correct option is A (ab)nFor any non-zero integers a and b, anbn=(ab)n, where 'n' is any integer. For example, 2−2−3−2=(−23)−2

$\frac{a^{n}}{b^{n}} =$ _____

The correct option is A $(\frac{a}{b})^{n}$
For any non-zero integers a and b,
$\frac{a^{n}}{b^{n}} = (\frac{a}{b})^{n}$ ,
where 'n' is any integer.
For example,
$\frac{2^{- 2}}{- 3^{- 2}} = (- \frac{2}{3})^{- 2}$