Answered

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Consider the expression:
[tex]\[ \frac{6^7}{6^4} \][/tex]

1. Express each exponent in expanded form:
[tex]\[ \frac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6 \cdot 6} \][/tex]

2. Divide common factors:

What is the exponent of the simplified power?

Sagot :

GinnyAnswer
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]
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