If \\( (7^x)^2\cdot 7^{x-1}=16807 \\), what is the value of \\(x\\)?
Answer and explanation
Correct answer: 2
Using the laws of exponents, \\( (7^x)^2=7^{2x}\\), so the left-hand side becomes \\(7^{2x}\cdot7^{x-1}=7^{3x-1}\\). Also, \\(16807=7^5\\). Therefore, \\(3x-1=5\\), giving \\(3x=6\\) and hence \\(x=2\\). Exam tip: when multiplying powers with the same base, add their exponents.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
Using the laws of exponents, \\( (7^x)^2=7^{2x}\\), so the left-hand side becomes \\(7^{2x}\cdot7^{x-1}=7^{3x-1}\\). Also, \\(16807=7^5\\). Therefore, \\(3x-1=5\\), giving \\(3x=6\\) and hence \\(x=2\\). Exam tip: when multiplying powers with the same base, add their exponents.
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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