Simplify the Expression: 17^16 ÷ 17^20 Using Laws of Exponents

To solve the expression $\frac{17^{16}}{17^{20}}$, we can apply the Power of a Quotient Rule for Exponents. This rule states that when you divide two exponents with the same base, you can subtract the exponents to simplify the expression.

The given expression is:

$\frac{17^{16}}{17^{20}}$

According to the Quotient Rule for Exponents, this expression can be simplified as:

$17^{16-20}$

Here's the step-by-step breakdown:

• The base of both the numerator and the denominator is the same, that is, 17.
• According to the rule, subtract the exponent in the denominator from the exponent in the numerator: $16 - 20$.
• This gives us the exponent: $-4$.

So, the simplified expression is:

$17^{-4}$

However, as requested, we should express this as:

$17^{16-20}$

The solution to the question is:

$17^{16-20}$