Simplify ( (x^2)^3 \times x^{-1} )
Answer and explanation
Correct answer: x^5
Using the power-of-a-power rule, \((x^2)^3=x^{2\times3}=x^6\). Then, for the product of powers with the same base, \(x^m\times x^n=x^{m+n}\), so \(x^6\times x^{-1}=x^{6+(-1)}=x^5\). Therefore, the correct answer is x^5. Exam tip: when adding exponents, include the negative sign; treating
\(x^{-1}\) as \(x^1\) would incorrectly give x^7.
Frequently asked questions
What is the correct answer to this question?
x^5
Why is this the correct answer?
Using the power-of-a-power rule, \((x^2)^3=x^{2\times3}=x^6\). Then, for the product of powers with the same base, \(x^m\times x^n=x^{m+n}\), so \(x^6\times x^{-1}=x^{6+(-1)}=x^5\). Therefore, the correct answer is x^5. Exam tip: when adding exponents, include the negative sign; treating
\(x^{-1}\) as \(x^1\) would incorrectly give x^7.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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