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Exponents with Unlike Bases and Same Exponent

Question 20 F...

Question

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

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Solution

We know that,
$a^{m} \div a^{n} = a^{m - n}, (m > n) S o, {(\frac{a}{b})}^{m} \div {(\frac{a}{b})}^{n} = {(\frac{a}{b})}^{m - n}$

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Similar questions

a

b

are non-zero integers,

m

n

are any integers, then which of the following are true?

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

\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}

$a b - m n + a n - b m = ? (a) (a - b) (m - n) (b) (a - m) (b + n) (c) (a - n) (m + b) (d) (m - a) (n - b)$

Q. Tick (✓) the correct answer:
ab − mn + an − bm = ?
(a) (a − b)(m − n)
(b) (a − m)(b + n)
(c) (a − n)(m + b)
(d) (m − a)(n − b)

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Exponents with Unlike Bases and Same Exponent

Standard VIII Mathematics

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