For non-zero numbers a and b- -a-b-m - -a-b-n- where m-n- is equal to -a- -a-b-mn -b- -a-b-m - n -c- -a-b-m - n- -d- -a-b-m-n - Maths Q-A

Evaluate the expression:The given expression is,(a/b)^m÷(a/b)^n=a^m/b^m÷a^n/b^n =a^m/b^m×b^n/a^n ...

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Byju's Answer

Standard VII

Mathematics

a^m / b^m = (a/b)^m

For non-zero ...

Question

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

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

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

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

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

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Solution

The correct option is C
${(\frac{a}{b})}^{m - n}$

Evaluate the expression:
The given expression is,
${(\frac{a}{b})}^{m} \div {(\frac{a}{b})}^{n} = \frac{a^{m}}{b^{m}} \div \frac{a^{n}}{b^{n}}$
$= \frac{a^{m}}{b^{m}} \times \frac{b^{n}}{a^{n}}$
$= \frac{a^{m}}{a^{n}} \times \frac{b^{n}}{b^{m}}$
$= a^{m - n} \times b^{n - m}$ $[∵ \frac{1}{a^{x}} = a^{- x}; a^{x} \times a^{y} = a^{x + y}]$
$= a^{m - n} \times b^{- (m - n)}$
$= \frac{a^{m - n}}{b^{m - n}}$
$= {(\frac{a}{b})}^{m - n}$
Hence, the required answer is ${(\frac{a}{b})}^{m - n}$ and therefore option $(C)$ is the correct answer.

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

The correct option is C abm-nEvaluate the expression:The given expression is,abm÷abn=ambm÷anbn =ambm×bnan =aman×bnbm =am-n×bn-m ∵1ax=a-x;ax×ay=ax+y =am-n×b-m-n =am-nbm-n =abm-nHence, the required answer is abm-n and therefore option C is the correct answer.

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