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Mathematics

Operations on real numbers and the laws of exponents

वास्तविक संख्याओं पर संक्रियाएँ और घातांक के नियम

In this Class 10 Mathematics topic from the Polynomials chapter, students strengthen their understanding of operations on real numbers and the laws of exponents. They learn to add, subtract, multiply and divide numerical expressions accurately, use exponent rules for products, quotients and powers, and simplify expressions involving positive, zero and negative exponents where appropriate. The topic builds fluency in working with polynomial terms, comparing equivalent forms, and checking calculations through properties such as commutativity, associativity and distributivity. Examples connect numerical rules with algebraic manipulation and related exercises.

Practice questions

Using an algebraic identity, find the value of \(72\cdot68\).MediumLevel 45 What is the value of \(3.5^2-2.5^2\)?EasyLevel 45 If \(a=2\) and \(b=5\), what is the value of \(a^2b+ab^2\)?MediumLevel 45 What is the factorized form obtained by taking the common factor out of \(4x^5+12x^4\)?MediumLevel 45 For a non-zero base \(a\), which rule represents division of powers with the same base?MediumLevel 45 If \(x=4\), what is the value of \(x^3-3x^2+2x\)?MediumLevel 45 If \(x=-4\), what is the value of \(x^4+x^3\)?MediumLevel 45 If \(x\neq0\) and \(y\neq0\), what is the simplified form of \(\frac{x^8y^{-4}}{x^5y^{-6}}\)?MediumLevel 45 If \(a\neq0\) and \(b\neq0\), what is the simplified form of \(\left(\frac{a^{-2}}{b^{-4}}\right)^{-1}\)?MediumLevel 45 What is the value of \(\left(5^2\right)^0+2^{-3}\)?MediumLevel 45 For a non-zero base \(a\), which law of exponents is represented by \(a^m \div a^n=a^{m-n}\)?MediumLevel 45 What is the value of \(2^7\cdot16^{-1}\)?MediumLevel 45 What is the expansion of \((4x-5)^2\)?MediumLevel 45 What is the expansion of \\((5x+2)^2\\)?MediumLevel 45 What is the simplified form of (7x+6)(7x-6)?MediumLevel 45 If \(3^{x+2}=243\), what is the value of \(x\)?MediumLevel 45 If \(2^{x-1}=32\), what is the value of \(x\)?MediumLevel 45 What is the simplest value of \(\frac{(2^4)^2\cdot 8^{-1}}{4}\)?MediumLevel 45 What is the factorized form of \(100x^2-121y^2\)?MediumLevel 45 If \(x\neq0\) and \(y\neq0\), what is the simplest form of \(\frac{(2x^2y^{-2})^3}{8x^3y^{-7}}\)?MediumLevel 45