Question 5Find the value of m for which5m - 5-3-55

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Standard VIII

Mathematics

Laws of Exponents

Question 5Fin...

Question

Question 5
Find the value of m for which
$5^{m} \div 5^{- 3} = 5^{5}$

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Solution

$5^{m} \div 5^{- 3} = 5^{5} \Rightarrow 5^{m - (- 3)} = 5^{5} [∵ a^{m} \div a^{n} = a^{m - n}] \Rightarrow 5^{m + 3} = 5^{5}$
On both the sides powers have the same base, so their exponents must be equal.
$\Rightarrow$ m+3=5
$\Rightarrow$ m = 5 - 3
$\Rightarrow$ m = 2

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Laws of Exponents

Standard VIII Mathematics

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Question 5 Find the value of m for which 5m÷5−3=55

5m÷5−3=55⇒ 5m−(−3)=55 [∵ am÷an=am−n]⇒5m+3=55 On both the sides powers have the same base, so their exponents must be equal. ⇒ m+3=5 ⇒ m = 5 - 3 ⇒ m = 2

Question 5
Find the value of m for which
$5^{m} \div 5^{- 3} = 5^{5}$

$5^{m} \div 5^{- 3} = 5^{5} \Rightarrow 5^{m - (- 3)} = 5^{5} [∵ a^{m} \div a^{n} = a^{m - n}] \Rightarrow 5^{m + 3} = 5^{5}$
On both the sides powers have the same base, so their exponents must be equal.
$\Rightarrow$ m+3=5
$\Rightarrow$ m = 5 - 3
$\Rightarrow$ m = 2