If \(x\ne0\), what is the simplified form of \(\frac{x^7\cdot x^{-3}}{x^2}\)?
Answer and explanation
Correct answer: \(x^2\)
For powers with the same nonzero base, exponents are added during multiplication and subtracted during division. Thus, \(\frac{x^7\cdot x^{-3}}{x^2}=x^{7+(-3)-2}=x^2\). Option C results from simplifying only \(x^7\cdot x^{-3}\) and ignoring the division by \(x^2\). Exam tip: subtract the denominator’s exponent when dividing like bases.
Frequently asked questions
What is the correct answer to this question?
\(x^2\)
Why is this the correct answer?
For powers with the same nonzero base, exponents are added during multiplication and subtracted during division. Thus, \(\frac{x^7\cdot x^{-3}}{x^2}=x^{7+(-3)-2}=x^2\). Option C results from simplifying only \(x^7\cdot x^{-3}\) and ignoring the division by \(x^2\). Exam tip: subtract the denominator’s exponent when dividing like bases.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
