Answer :
Let's solve the given expression step-by-step.
Given expression:
[tex]\[ \frac{6^7}{6^4} \][/tex]
1. Express each exponent in expanded form:
[tex]\[ \frac{6^7}{6^4} = \frac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6 \cdot 6} \][/tex]
2. Divide the common factors from the numerator and the denominator:
[tex]\[ \frac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6 \cdot 6} = 6 \cdot 6 \cdot 6 \][/tex]
After canceling out the common \(6\)s from the numerator and the denominator, we are left with:
[tex]\[ 6 \cdot 6 \cdot 6 = 6^3 \][/tex]
Thus, the exponent of the simplified power is:
[tex]\[ 3 \][/tex]
Given expression:
[tex]\[ \frac{6^7}{6^4} \][/tex]
1. Express each exponent in expanded form:
[tex]\[ \frac{6^7}{6^4} = \frac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6 \cdot 6} \][/tex]
2. Divide the common factors from the numerator and the denominator:
[tex]\[ \frac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6 \cdot 6} = 6 \cdot 6 \cdot 6 \][/tex]
After canceling out the common \(6\)s from the numerator and the denominator, we are left with:
[tex]\[ 6 \cdot 6 \cdot 6 = 6^3 \][/tex]
Thus, the exponent of the simplified power is:
[tex]\[ 3 \][/tex]
