What is the correct simplified form of \((a^3b^2)^3\)?
Answer and explanation
Correct answer: \(a^9b^6\)
Using the exponent law \((xy)^n=x^ny^n\), the outer exponent 3 multiplies the exponent of each factor: \((a^3b^2)^3=a^{3\times3}b^{2\times3}=a^9b^6\). Therefore, option A is correct. In option C, only the exponent of \(a\) is multiplied, while the exponent of \(b\) is incorrectly left as 2. Exam tip: when a power applies to a product, distribute it to every factor and multiply the exponents.
Frequently asked questions
What is the correct answer to this question?
\(a^9b^6\)
Why is this the correct answer?
Using the exponent law \((xy)^n=x^ny^n\), the outer exponent 3 multiplies the exponent of each factor: \((a^3b^2)^3=a^{3\times3}b^{2\times3}=a^9b^6\). Therefore, option A is correct. In option C, only the exponent of \(a\) is multiplied, while the exponent of \(b\) is incorrectly left as 2. Exam tip: when a power applies to a product, distribute it to every factor and multiply the 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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
