Question

If 36^m × (216)^–2 = 6, then the value of m is

(1) 5

(2) 7 /2

(3) –4

(4) 9/2​

Answer 1

Answer:

c option is correct and

Answer 2

$Given \:36^{m} \times (216)^{-2} = 6$

$\implies ( 6^{2} )^{m} \times (6^{3})^{-2} = 6$

$\implies 6 ^{2m} \times 6^{3 \times (-2)} = 6$

$\boxed { \pink { Since , (a^{m})^{n} = a^{m \times n } }}$

$\implies 6^{2m} \times 6^{-6} = 6$

$\implies 6^{2m- 6} = 6^{1}$

$\boxed { \blue { Since , a^{m} \times a^{n} = a^{m + n } }}$

$\implies 2m - 6 = 1$

$\implies 2m = 1 + 6$

$\implies 2m = 7$

$\implies m = \frac{7 }{2}$

Therefore.,

$\red{ Value \:of \: m } \green { = \frac{7 }{2}}$

$Option \: \pink { ( 2 ) } \: is \: correct.$

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