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
If \(x\neq0\) and \(y\neq0\), what is the simplified form of \(\frac{(3x^2y^{-1})^2}{9xy^{-3}}\)?What is the simplified form of \(5^4\cdot5^{-2}\cdot5^3\)?What is the simplified form of \(\frac{7^3}{7^{-1}\cdot 7^2}\)?If \(x\neq 0\), what is the simplified form of \(\frac{(x^2)^3\cdot x^{-1}}{x^2}\)?According to the laws of exponents, which rule applies when a term with an exponent,
a^m, is raised to the nth power?Which of the following statements correctly represents a law of exponents for all positive real numbers \(a\) and \(b\) and any real number \(r\)?What is the value of (0.25)^{-2}?What is the value of \(\left(\frac{4}{3}\right)^{-2}\cdot\left(\frac{16}{9}\right)\)?If \(a=3\), what is the value of \(a^2+a^{-1}\)?What is the correct simplified form of \((a^3b^2)^3\)?If \(x\neq0\), what is the simplified form of \(\frac{(3x^2)^2}{9x}\)?For a non-zero real number \(a\) and a positive integer \(n\), which of the following is the correct law of negative exponents?If q(x) = 2x³ + x² − 3x, what is the value of q(−1)?What is the simplified form of \\(4x^3+7x^3-5x^3\\)?What is the simplified form of the expression ((2x + 3) + (4x - 7))?What is the simplified form of \\((7x-2)-(3x+5)\\)?What is the expanded form of the polynomial \(3x(2x^2-5x+4)\)?What is the expansion of (x+4)(x+3)?For a non-zero real number \(a\) and integers \(m,n\), which equation correctly represents the product law of exponents?What is the expansion of (3x+1)(x-4)?