Question

SIMPLIFYING EXPRESSIONS Simplify the expression. $$ \frac{7^{4} \cdot 7}{7^{7}} $$

Short answer

So, the simplified form of the expression is \(7^{-2}\).

Step-by-step solution

Understand exponentiation rules

The first step implies recognizing the rule \(a^{m} \cdot a^{n} = a^{m+n}\). This rule allows us to add exponents when the bases are the same.

Apply the rule

Apply the rule to the given expression. The base '7' is the same for all parts of the equation. This means we can add the exponent '4' and '1' (representing \(7^{4} \cdot 7\)) to get the exponent '5'. So the expression becomes \(7^{5}/7^{7}\).

Simplify the expression

Finally, use the rule \(a^{m}/a^{n} = a^{m-n}\) to subtract the exponent in the denominator from the exponent in the numerator. So the expression becomes \(7^{5-7} = 7^{-2}\).