The relation xm-xn-xm-n is true- if x-0 and m- n-

Checking by taking examplesx^m÷x^n=x^m nLet us take x=5, m=4 and n=65^4÷5^6=5^4 6LHS ⇒5^4÷5^6=5^4/5^6=1/5^6 4=1/5^2RHS ⇒5^4 6=5^ 2=1/5^2Therefore , LHS=RHSHence ...

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Byju's Answer

Standard VIII

Mathematics

Exponents with Unlike Bases and Same Exponent

The relation ...

Question

The relation $x^{m} \div x^{n} = x^{m - n}$ is true, if $x > 0$ and $m \leq n$ .

True

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False

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Solution

The correct option is A True
Checking by taking examples
$x^{m} \div x^{n} = x^{m - n}$
Let us take $x = 5, m = 4 a n d n = 6$
$5^{4} \div 5^{6} = 5^{4 - 6}$
LHS $\Rightarrow 5^{4} \div 5^{6} = \frac{5^{4}}{5^{6}} = \frac{1}{5^{6 - 4}} = \frac{1}{5^{2}}$
RHS $\Rightarrow 5^{4 - 6} = 5^{- 2} = \frac{1}{5^{2}}$
Therefore , LHS $=$ RHS
Hence, $x^{m} \div x^{n} = x^{m - n}$ is true, if $x > 0$ and $m \leq n$ .

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The relation xm÷xn=xm-n is true, if x>0 and m≤n.

The correct option is A TrueChecking by taking examplesxm÷xn=xm-nLet us take x=5,m=4andn=654÷56=54-6LHS ⇒54÷56=5456=156-4=152RHS ⇒54-6=5-2=152Therefore , LHS=RHSHence, xm÷xn=xm-n is true, if x>0 and m≤n.

The relation $x^{m} \div x^{n} = x^{m - n}$ is true, if $x > 0$ and $m \leq n$ .