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Answer
The expression simplifies to \( \frac{1}{49} \).
Solution
To simplify (7^(3a - 1))/(7^(3a + 1)), subtract the exponent in the denominator from the exponent in the numerator:
(3a - 1) - (3a + 1) = 3a - 1 - 3a - 1 = -2
This gives 7^(–2), which can also be written as 1/7² or 1/49.
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Simplify this solution The Deep Dive
To simplify the expression \( \frac{7^{3 a-1}}{7^{3 a+1}} \), you can utilize the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \). So, you subtract the exponents: \[ \frac{7^{3 a-1}}{7^{3 a+1}} = 7^{(3 a - 1) - (3 a + 1)}. \] This simplifies to: \[ 7^{(3 a - 1 - 3 a - 1)} = 7^{-2}. \] Thus, the simplified form is: \[ \frac{1}{7^2} = \frac{1}{49}. \] Now you have a sleek expression that presents the same value in a more digestible format!
