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Ex.12.1 Q5 Exponents and Powers Solution - NCERT Maths Class 8

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Question

Find the value of m for which \(\begin{align}({5^m} \div {5^{ - 3}}) = {5^5}\end{align}\)

 Video Solution
Exponents And Powers
Ex 12.1 | Question 5

Text Solution

What is known?

Expression in exponential form

What is unknown?

Value of \(m\)

Reasoning:

\[{a^m} \div {a^n} = {a^{m - n}}\]

Steps:

\[\begin{align}({5^m} \div {5^{ - 3}})&= {5^5}\\{5^{m - ( - 3)}} &= {5^5}\\{5^{m + 3}} &= {5^5}\end{align}\]

On both the side powers have the same base, so their exponents must be equal.

\(\therefore + 3 = 5 \to m = 5 - 3 \to m = 2\)

  
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