Prove that- abmabn - abm-n

We have, (ab)^m(ab)^n =a^m.b^na^nb^m =a^m nb^m n =(ab)^m n ...

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Standard VII

Mathematics

Exponents with Unlike Bases and Same Exponent

Prove that: ...

Question

Prove that: $\frac{{(\frac{a}{b})}^{m}}{{(\frac{a}{b})}^{n}} = {(\frac{a}{b})}^{m - n}$

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Solution

We have,
$\frac{{(\frac{a}{b})}^{m}}{{(\frac{a}{b})}^{n}}$
$= \frac{a^{m} . b^{n}}{a^{n} b^{m}}$
$= \frac{a^{m - n}}{b^{m - n}}$
$= {(\frac{a}{b})}^{m - n}$

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Similar questions

Q. Show that:

\frac{{(a + \frac{1}{b})}^{m} \times {(a - \frac{1}{b})}^{n}}{{(b + \frac{1}{a})}^{m} \times {(b - \frac{1}{a})}^{n}} = {(\frac{a}{b})}^{m + n}

Question 20

For non-zero numbers $a$ and $b$ , ${(\frac{a}{b})}^{m} \div {(\frac{a}{b})}^{n},$ where $m > n,$ is equal to:
(a) ${(\frac{a}{b})}^{m n}$
(b) ${(\frac{a}{b})}^{m + n}$
(c) ${(\frac{a}{b})}^{m - n}$
(d) ${({(\frac{a}{b})}^{m})}^{n}$

Q. ABCD is a rectangle. Point M or N are on BD such that

A M ⊥ B D

and

C N ⊥ B D .

Prove that

{B M}^{2} + {B N}^{2} = {D M}^{2} + {D N}^{2} .

Q. The altitude

B N

and

C M

△ A B C

meet at

H

. Prove that
(i)

C N \times H M = B M \times H N

(ii)

H C / H B = \sqrt{[(C N \times H N) / (B M \times H M)]}

(iii)

△ M H N \sim △ B H C

Q. In the given figure, BM = BN, M is the mid point of AB and N is the mid point of BC. Then BM = ____________ ?

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Prove that: (ab)m(ab)n=(ab)m−n

We have,(ab)m(ab)n=am.bnanbm=am−nbm−n=(ab)m−n

Prove that: $\frac{{(\frac{a}{b})}^{m}}{{(\frac{a}{b})}^{n}} = {(\frac{a}{b})}^{m - n}$

We have,
$\frac{{(\frac{a}{b})}^{m}}{{(\frac{a}{b})}^{n}}$
$= \frac{a^{m} . b^{n}}{a^{n} b^{m}}$
$= \frac{a^{m - n}}{b^{m - n}}$
$= {(\frac{a}{b})}^{m - n}$