The value of m is 8.
Step-by-step explanation:
The given expression is that [tex]4^{m}/4^{5} = 4^{3}[/tex]
We know that, the m, 5, 3 are exponents which represents the power of the base number. Here, 4 is the base in this given expression.
To find the value of m :
The first step is to equate the exponents on both sides of the expression.
Before that, bring the denominator [tex]4^{5}[/tex] to the numerator by changing the sign of the exponent.
For example, [tex]a^{m} /a^{n} = a^{m-n[/tex]
⇒ [tex]4^{m-5} = 4^{3}[/tex]
Now, if the bases are same then it is possible to equate the exponents on both sides of the expression.
The exponent on the left side of expression is (m-5) and the exponent on the right side is 3.
⇒ m-5 = 3
Add 5 on both sides,
⇒ m-5+5 = 3+5
⇒ m = 8
Therefore, the value of m is 8.
