Question

If , (pic attached ) then find the value of m.

Answer 1

Step-by-step explanation:

please mark the answer as brainliest

Answer 2

$\dfrac{5^{m}\times 5^{3}\times 5^{-2} }{5^{-5}} =5^{12}$

First, we will have to apply this law of exponent to find 'm' ⇒ $a^{m}\times a^{n}=a^{m+n}$

⇒ $\dfrac{5^{m}\times 5^{3}\times 5^{-2} }{5^{-5}} =5^{12}$

⇒ $\dfrac{5^{m}\times 5^{3+-2} }{5^{-5}} =5^{12}$

⇒ $\dfrac{5^{m}\times 5^{3-2} }{5^{-5}} =5^{12}$

⇒ $\dfrac{5^{m}\times 5^{1} }{5^{-5}} =5^{12}$

Now, we will apply this law of exponent to find 'm' ⇒ $a^{m}\div a^{n}=a^{m-n}$

⇒ $\dfrac{5^{m}\times 5^{1} }{5^{-5}} =5^{12}$

⇒ $5^{m}\times 5^{1--5} =5^{12}$

⇒ $5^{m}\times 5^{1+5} =5^{12}$

⇒ $5^{m}\times 5^{6} =5^{12}$

Since the bases are same, we'll take only the exponents and solve. We'll have to keep this law of exponent in mind while solving ⇒ $a^{m}\times a^{n}=a^{m+n}$.

Let's solve your equation step-by-step.

$m+6=12$

Step 1: Subtract 6 from both sides of the equation.

⇒ $m+6=12$

⇒ $m+6-6=12-6$

⇒ $m=6$

∴ The value of 'm' is 6.

Let's verify is 6 is really the value of 'm'.

⇒ $\dfrac{5^{m}\times 5^{3}\times 5^{-2} }{5^{-5}} =5^{12}$

⇒$\dfrac{5^{6}\times 5^{3}\times 5^{-2} }{5^{-5}} =5^{12}$

We'll apply this law of exponent ⇒ $a^{m}\times a^{n}=a^{m+n}$

⇒ $\dfrac{5^{6+3+-2} }{5^{-5}} =5^{12}$

⇒ $\dfrac{5^{6+3-2} }{5^{-5}} =5^{12}$

⇒ $\dfrac{5^{9-2} }{5^{-5}} =5^{12}$

⇒ $\dfrac{5^{7} }{5^{-5}} =5^{12}$

We'll apply this law of exponent ⇒ $a^{m}\div a^{n}=a^{m-n}$

⇒ $\dfrac{5^{7} }{5^{-5}} =5^{12}$

⇒ $5^{7--5}=5^{12}$

⇒ $5^{7+5}=5^{12}$

⇒ $5^{12}=5^{12}$

Hence, verified.