Question

I-2
10. Find the value of m for which 9^m ÷ 3^-2 = 9^4​

Answer 1

Answer:

value of m is 3

Step-by-step explanation:

this is the common solution

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Answer 2

Answer:

m = 3

Step-by-step explanation:

Using laws of Indices

${x}^{y} \times {x}^{a} = {x}^{y + a} \\ \\ \frac{ {x}^{n} }{ {x}^{m} } = {x}^{n - m} \\ \\ {x}^{ - 1} = \frac{1}{x} \\ \\ { 3}^{x} = {3}^{y} \: \: \: \: \: \: \: x = y$

Solution:

${9}^{m} \div {3}^{( - 2) }= {9}^{4} \\ \\ { ({3}^{2} )}^{m} \div \frac{1}{ {3}^{2} } = {( {3}^{2}) }^{4} \\ \\ {3}^{2m} \times {3}^{2} = {3}^{8} \\ \\ {3}^{2m + 2} = {3}^{8} \\ \\ 2m + 2 = 8 \\ \\ 2m = 8 - 2 \\ \\ \cancel{2}m = \cancel{6} \\ \\ m \: = 3$

Hence, The required value of m is 3 .