Complete the Expression: Base 20 Raised to Power 6y

Insert the corresponding expression:

$20^{6y}=$

To solve the given expression $20^{6y}$ and express it as a fraction $\frac{a^m}{a^n}$, we can use the Power of a Quotient Rule for Exponents. This rule states that:

• $\frac{a^m}{a^n} = a^{m-n}$

We have the expression $20^{6y}$ which we want to represent as $\frac{20^{m}}{20^{n}}$.

To achieve this, we must have:

• $m - n = 6y$

A straightforward way to do this is to choose $m = 10y$ and $n = 4y$, such that:

• $10y - 4y = 6y$

This choice satisfies the equation $m - n = 6y$, thus the given expression can be rewritten using the power of a quotient rule as:

$20^{6y} = \frac{20^{10y}}{20^{4y}}$

This confirms that expressing $20^{6y}$ as $\frac{20^{10y}}{20^{4y}}$ is consistent with the given correct answer.

The solution to the question is: $\frac{20^{10y}}{20^{4y}}$