Applying the Quotient Rule of Exponents, what is the exponent in an equivalent form of (5/6)^10÷(5/6)^3

Question

(
5
6
)
10
÷
(
5
6
)
3
? Answer with a whole number for the exponent.(1 point)

Answer 1

To solve the expression \((\frac{5}{6})^{10} \div (\frac{5}{6})^{3}\), we can apply the Quotient Rule of Exponents. The Quotient Rule states that when you divide two exponential expressions with the same base, you subtract the exponents:

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

In this case, \(m = 10\) and \(n = 3\). Thus, we have:

\[ (\frac{5}{6})^{10} \div (\frac{5}{6})^{3} = (\frac{5}{6})^{10-3} \]

Calculating \(10 - 3\) gives us \(7\). Therefore, the expression simplifies to:

\[ (\frac{5}{6})^{7} \]

The exponent in this equivalent form is \(\boxed{7}\).