Apply the Quotient Rule of Exponents to simplify 9^8/9^6

Question

as an equivalent expression.

Answer 1

To simplify \(\frac{9^8}{9^6}\) using the Quotient Rule of Exponents, we use the rule which states that:

\[ \frac{a^m}{a^n} = a^{m-n} \]

In this case, we have:

• \(a = 9\)
• \(m = 8\)
• \(n = 6\)

Applying the Quotient Rule:

\[ \frac{9^8}{9^6} = 9^{8-6} = 9^2 \]

Now, we can simplify \(9^2\):

\[ 9^2 = 81 \]

Thus, the equivalent expression for \(\frac{9^8}{9^6}\) is:

\[ 9^2 \quad \text{or} \quad 81 \]