If \(x\neq0\), what is the simplified form of \(\frac{(x^3)^2\cdot x^{-4}}{x}\)?
Answer and explanation
Correct answer: \(x\)
Using the power-of-a-power rule, \((x^3)^2=x^{3\times2}=x^6\). For the remaining product and division of powers with the same base, subtract the denominator exponent: \(x^6\cdot x^{-4}\div x=x^{6-4-1}=x\). Therefore, option A is correct. Exam tip: write the denominator as \(x^1\) before combining exponents.
Frequently asked questions
What is the correct answer to this question?
\(x\)
Why is this the correct answer?
Using the power-of-a-power rule, \((x^3)^2=x^{3\times2}=x^6\). For the remaining product and division of powers with the same base, subtract the denominator exponent: \(x^6\cdot x^{-4}\div x=x^{6-4-1}=x\). Therefore, option A is correct. Exam tip: write the denominator as \(x^1\) before combining 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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