What is the value of \((10^{1}\times10^{2})\)?
Answer and explanation
Correct answer: 1000
Use the law of exponents: when bases are equal, add the exponents: \(a^{m}\times a^{n}=a^{m+n}\). Here base 10 with exponents 1 and 2 gives \(10^{1}\times10^{2}=10^{1+2}=10^{3}=1000\). Option B (100) would result from the mistake of multiplying or ignoring exponents (or taking only \(10^2\)). Options A and D are also incorrect and reflect common calculation errors. Exam tip: convert factors to powers of the same base and add exponents; a quick check: \(10\times100=1000\).
Frequently asked questions
What is the correct answer to this question?
1000
Why is this the correct answer?
Use the law of exponents: when bases are equal, add the exponents: \(a^{m}\times a^{n}=a^{m+n}\). Here base 10 with exponents 1 and 2 gives \(10^{1}\times10^{2}=10^{1+2}=10^{3}=1000\). Option B (100) would result from the mistake of multiplying or ignoring exponents (or taking only \(10^2\)). Options A and D are also incorrect and reflect common calculation errors. Exam tip: convert factors to powers of the same base and add exponents; a quick check: \(10\times100=1000\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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