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Subjects

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 \(x\neq0\), what is the simplified form of \(\frac{(2x^3)^2}{4x^2}\)?MediumLevel 43If \(p(x)=2x^2-3x+1\), what is the value of \(p(2)\)?MediumLevel 43If \(q(x)=x^3-2x^2+x\), what is the value of \(q(-1)\)?MediumLevel 43What is the simplified form of (3x^2 + 5x^2 - 2x^2)?MediumLevel 43If \(a\neq 0\), what is the simplified form of \(\dfrac{a^7}{a^3}\)?MediumLevel 43If \(a\) is a non-zero real number and \(m\) and \(n\) are integers, which is the correct law for multiplying powers with the same base?MediumLevel 43What is the expanded form of the algebraic expression 2x(3x^2-4x+1)?MediumLevel 43What is the expanded and simplified form of 8x+39(x+2)?MediumLevel 43If \(a\neq 0\), what is the simplest form of \(\frac{(a^4)^3}{a^5}\)?MediumLevel 43What is the expansion of \( (2x+3)(x-2) \)?MediumLevel 43For a non-zero real number \(a\) and integers \(m,n\), which of the following represents the quotient law of exponents?MediumLevel 43What is the correct expansion of 8x-69^2?MediumLevel 43What is the simplified form of \((x+7)(x-7)\)?MediumLevel 43What is the factorized form of \(49x^2-64\)?MediumLevel 43Which of the following is equal to the expression \(x^2+14x+49\)?MediumLevel 43Which of the following is equal to the expression \(x^2-16x+64\)?MediumLevel 43If \(m+n=9\) and \(mn=18\), what is the value of \(m^2+n^2\)?MediumLevel 43If \(a-b=5\) and \(ab=6\), what is the value of \(a^2+b^2\)?MediumLevel 43Using the identity \((a-b)^2=a^2-2ab+b^2\), what is the value of \(99^2\)?MediumLevel 43In which of the following expressions has the product rule of exponents been applied correctly?MediumLevel 43