Question
Download Solution PDFFind the value of \( \left(\frac{1}{7}\right)^{-4} + \left(\frac{1}{9}\right)^{-4} + \left(\frac{1}{5}\right)^{-4} \)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Find the value of \(\left(\dfrac{1}{7}\right)^{-4} + \left(\dfrac{1}{9}\right)^{-4} + \left(\dfrac{1}{5}\right)^{-4} \)
Formula used:
\(\left(\dfrac{a}{b}\right)^{-n} = \left(\dfrac{b}{a}\right)^{n} \)
Calculation:
\(\left(\dfrac{1}{7}\right)^{-4} + \left(\dfrac{1}{9}\right)^{-4} + \left(\dfrac{1}{5}\right)^{-4} \)
⇒ \(\left(\dfrac{7}{1}\right)^{4} + \left(\dfrac{9}{1}\right)^{4} + \left(\dfrac{5}{1}\right)^{4} \)
⇒ 74 + 94 + 54
⇒ 2401 + 6561 + 625
⇒ 2401 + 6561 + 625 = 9587
∴ The correct answer is option (3).
Last updated on Jun 21, 2025
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