Questions: Simplify using the quotient rule. Then evaluate. 6^14 / 6^11 6^14 / 6^11 = (Type an integer or a simplified fraction.)

$Simplify using the quotient rule. Then evaluate. 6^14 / 6^11 6^14 / 6^11 = (Type an integer or a simplified fraction.)$

Transcript text: Simplify using the quotient rule. Then evaluate. \[ \frac{6^{14}}{6^{11}} \] $\frac{6^{14}}{6^{11}}=$ $\square$ (Type an integer or a simplified fraction.)

Solution

Solution Steps

To simplify the given expression using the quotient rule of exponents, we subtract the exponent in the denominator from the exponent in the numerator. The quotient rule states that $\frac{a^m}{a^n} = a^{m-n}$. After simplifying, we can evaluate the result.

Step 1: Apply the Quotient Rule

Using the quotient rule of exponents, we simplify the expression $\frac{6^{14}}{6^{11}}$ as follows: \[ \frac{6^{14}}{6^{11}} = 6^{14 - 11} = 6^{3} \]

Step 2: Evaluate the Exponent

Next, we evaluate $6^{3}$: \[ 6^{3} = 6 \times 6 \times 6 = 216 \]