Question
Simplify the following expression. \( 7^{-4}=\square \) (Type a simplified fraction.)
Ask by Vaughn Floyd. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 7^{-4} = \frac{1}{7^4} = \frac{1}{2401} \)
Solution
Calculate or simplify the expression \( 7^{-4} \).
Calculate the value by following steps:
- step0: Calculate:
\(7^{-4}\)
- step1: Express with a positive exponent:
\(\frac{1}{7^{4}}\)
- step2: Evaluate the power:
\(\frac{1}{2401}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To simplify \( 7^{-4} \), we can use the rule of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \). So, \( 7^{-4} = \frac{1}{7^4} \). Next, we calculate \( 7^4 \): \[ 7^4 = 7 \times 7 \times 7 \times 7 = 2401. \] Thus, \( 7^{-4} = \frac{1}{2401} \). So, the simplified expression is \( \frac{1}{2401} \).
