Question

Help me guy, my exam is going on ​

Answer 1

Answer:

m = 6

Step-by-step explanation:

$\frac{5^m*5^3*5^{-2}}{5^{-5}} = 5^{12}$

By applying the rules of indices

$a^m*a^n = a^{m+n}$

⇒ $\frac{5^{m+3-2}}{5^{-5}} = 5^{12}$

⇒ $\frac{5^{m+1}}{5^{-5}} = 5^{12}$

⇒ $5^{m+1+5} = 5^{12}$

If bases are same powers are also same and vise versa

$m + 6 = 12$

⇒ m = 6

Answer 2

m = 6

Step-by-step explanation:

\frac{5^m*5^3*5^{-2}}{5^{-5}} = 5^{12}

5

−5

5

m

∗5

3

∗5

−2

=5

12

By applying the rules of indices

a^m*a^n = a^{m+n}a

m

∗a

n

=a

m+n

⇒ \frac{5^{m+3-2}}{5^{-5}} = 5^{12}

5

−5

5

m+3−2

=5

12

⇒ \frac{5^{m+1}}{5^{-5}} = 5^{12}

5

−5

5

m+1

=5

12

⇒ 5^{m+1+5} = 5^{12}5

m+1+5

=5

12

If bases are same powers are also same and vise versa

m + 6 = 12m+6=12

⇒ m = 6