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Simplify the expression:

[tex]\[ \frac{3^6}{3^4} \][/tex]


Sagot :

To solve the expression [tex]\(\frac{3^6}{3^4}\)[/tex], follow these detailed steps:

1. Understand the properties of exponents:
We have the same base, which is [tex]\(3\)[/tex], in both the numerator and the denominator. The law of exponents states that when you divide like bases, you subtract the exponents:
[tex]\[ \frac{a^m}{a^n} = a^{m-n} \][/tex]

2. Apply the property to the given expression:
Here, [tex]\(a = 3\)[/tex], [tex]\(m = 6\)[/tex], and [tex]\(n = 4\)[/tex]. Substitute these values into the exponent rule:
[tex]\[ \frac{3^6}{3^4} = 3^{6-4} \][/tex]

3. Perform the subtraction in the exponent:
Subtract [tex]\(4\)[/tex] from [tex]\(6\)[/tex]:
[tex]\[ 6 - 4 = 2 \][/tex]

4. Simplify the expression:
Now we have:
[tex]\[ 3^{6-4} = 3^2 \][/tex]

5. Calculate the final result:
Evaluate [tex]\(3^2\)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]

Therefore, the result of [tex]\(\frac{3^6}{3^4}\)[/tex] is [tex]\(\boxed{9}\)[/tex].
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