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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

What is the value of \(0.65+0.25\)?EasyLevel 45 What is the value of (\frac{5}{6}+\frac{1}{12})?EasyLevel 45 What is the value of (\frac{5}{8}\cdot\frac{16}{15})?EasyLevel 45 What is the value of \(20-5\cdot3\)?EasyLevel 45 What is the value of the expression \(7+3^2\cdot5\)?EasyLevel 45 What is the simplified form of \(6x^2+8x^2\)?EasyLevel 45 What is the simplified form of (14x⁵ - 9x⁵)?EasyLevel 45 How many terms are there in the expression 6x + 7y + 4?EasyLevel 45 Which of the following is a like term of z⁴?EasyLevel 45 What is the product of \(5x^4 \cdot 2x^3\)?EasyLevel 45 If \(a\neq0\), what is the simplified form of \(42a^7\div6a^4\)?EasyLevel 45 What is the simplified form of \(7^2\cdot7^0\cdot7^4\)?EasyLevel 45 What is the simplified form of (\frac{2^3\cdot4^3}{8^2})?EasyLevel 45 Using the laws of exponents for like bases, what is the simplified form of \(2^3\cdot2^{-5}\cdot2^4\)?MediumLevel 43 What is the simplified form of \(\frac{3^2\cdot 3^{-4}}{3^{-3}}\)?MediumLevel 43 If \(x\neq0\), what is the simplified form of \(\frac{(x^3)^2\cdot x^{-4}}{x}\)?MediumLevel 43 According to the zero-exponent law, which of the following statements is correct?MediumLevel 43 What is the value of 8\frac{16^2}{2^5}9?MediumLevel 43 What is the value of \((0.2)^{-2}\)?MediumLevel 43 What is the value of \(\left(\frac{3}{2}\right)^{-2}\cdot\left(\frac{9}{4}\right)\)?MediumLevel 43