Questions: Perform the indicated operation and simplify your answer. 3^7 / 3^3 3^7 / 3^3 = (Type an integer or a simplified fraction.)

$Perform the indicated operation and simplify your answer. 3^7 / 3^3 3^7 / 3^3 = (Type an integer or a simplified fraction.)$

Transcript text: Perform the indicated operation and simplify your answer. \[ \begin{array}{l} \frac{3^{7}}{3^{3}} \\ \frac{3^{7}}{3^{3}}= \end{array} \] (Type an integer or a simplified fraction.)

Solution

Solution Steps

To simplify the expression $\frac{3^{7}}{3^{3}}$, we can use the properties of exponents. Specifically, when dividing like bases, we subtract the exponents. Therefore, the expression simplifies to $3^{7-3}$.

Step 1: Apply the Properties of Exponents

To simplify the expression $\frac{3^{7}}{3^{3}}$, we use the property of exponents that states $\frac{a^m}{a^n} = a^{m-n}$. Applying this property, we have:

\[ \frac{3^{7}}{3^{3}} = 3^{7-3} \]

Step 2: Simplify the Exponent

Subtract the exponents:

\[ 3^{7-3} = 3^{4} \]

Step 3: Calculate the Power

Calculate $3^{4}$:

\[ 3^{4} = 81 \]