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If \(\left(5^{x}\right)^{2}\cdot5^{x-2}=3125\), what is the value of (x)?
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Answer and explanation
Correct answer: \(\frac{7}{3}\)
The left side is \(5^{2x}\cdot5^{x-2}=5^{3x-2}\), and \(3125=5^{5}\). Hence \(3x-2=5\), so \(x=\frac{7}{3}\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{7}{3}\)
Why is this the correct answer?
The left side is \(5^{2x}\cdot5^{x-2}=5^{3x-2}\), and \(3125=5^{5}\). Hence \(3x-2=5\), so \(x=\frac{7}{3}\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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