What is the simplified form of \(\frac{7^3}{7^{-1}\cdot 7^2}\)?
Answer and explanation
Correct answer: \(7^2\)
For multiplication of powers with the same base, add the exponents: \(7^{-1}\cdot 7^2=7^{-1+2}=7^1\). Then divide powers with the same base by subtracting exponents: \(\frac{7^3}{7^1}=7^{3-1}=7^2\). Hence, option A is correct. Exam tip: add exponents when multiplying like bases and subtract them when dividing like bases.
Frequently asked questions
What is the correct answer to this question?
\(7^2\)
Why is this the correct answer?
For multiplication of powers with the same base, add the exponents: \(7^{-1}\cdot 7^2=7^{-1+2}=7^1\). Then divide powers with the same base by subtracting exponents: \(\frac{7^3}{7^1}=7^{3-1}=7^2\). Hence, option A is correct. Exam tip: add exponents when multiplying like bases and subtract them 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.
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