If \(a^m=2\) and \(a^n=7\), what is the value of \(a^{2m+n}\)?
Answer and explanation
Correct answer: 28
Using the laws of exponents, \(a^{2m+n}=a^{2m}\cdot a^n=(a^m)^2\cdot a^n\). Substituting the given values gives \(2^2\times 7=4\times 7=28\). Therefore, the correct answer is 28. In an exam, split a sum in the exponent into a product of powers; multiplying \(a^m\) and \(a^n\) directly would give 14, which corresponds to \(a^{m+n}\).
Frequently asked questions
What is the correct answer to this question?
28
Why is this the correct answer?
Using the laws of exponents, \(a^{2m+n}=a^{2m}\cdot a^n=(a^m)^2\cdot a^n\). Substituting the given values gives \(2^2\times 7=4\times 7=28\). Therefore, the correct answer is 28. In an exam, split a sum in the exponent into a product of powers; multiplying \(a^m\) and \(a^n\) directly would give 14, which corresponds to \(a^{m+n}\).
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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