Simplify the Expression: 16^(x+4)/16^3 Using Exponent Rules

To solve this problem, we need to simplify the given expression using the rules of exponents. The expression we have is:

$\frac{16^{x+4}}{16^3}$

According to the quotient rule for exponents, when dividing like bases, you subtract the exponent of the denominator from the exponent of the numerator. This is expressed as:

• $\frac{a^m}{a^n} = a^{m-n}$

In our problem, the base is 16, so we apply the quotient rule. We subtract the exponent 3 in the denominator from the exponent $x+4$ in the numerator:

$\frac{16^{x+4}}{16^3} = 16^{(x+4)-3}$

Simplify the exponent by performing the subtraction within the exponent:

$16^{(x+4)-3} = 16^{x+4-3} = 16^{x+1}$

Thus, the expression simplifies to:

$16^{x+1}$

The solution to the question is: $16^{x+1}$