Question
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Tutor-Verified Answer
Answer
\( 7^4 / 7^2 = 7^{4-2} = 7^2 = 49 \)
Solution
Calculate or simplify the expression \( 7^4 / 7^2 \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{7^{4}}{7^{2}}\)
- step1: Multiply by \(a^{-n}:\)
\(7^{4}\times 7^{-2}\)
- step2: Multiply:
\(7^{4-2}\)
- step3: Subtract the numbers:
\(7^{2}\)
- step4: Evaluate the power:
\(49\)
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Simplify this solution The Deep Dive
When diving powers with the same base, you can subtract the exponents. So, \( 7^{4} \div 7^{2} \) becomes \( 7^{(4-2)} \) or \( 7^{2} \). Simplifying further, \( 7^{2} = 49 \). Thus, the final answer is \( 49 \). This property showcases the elegance of exponents in mathematics. The rule of dividing powers, which is \( a^{m} \div a^{n} = a^{m-n} \), is crucial for simplifying expressions in algebra and beyond. It helps streamline calculations, making it easier to manipulate larger equations!
