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Algebraic Simplification

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsWhat is the simplified form of \(\frac{2a^{-1}+3a^{-1}}{5a^{-2}}\), where \(a\neq 0\)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 43Expert MathematicsIf (10^m · 100^2 / 1000 = 10^6), what is the value of (m)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 43Medium MathematicsWhat is the simplified form of (\frac{x^{-2}-y^{-2}}{x^{-1}-y^{-1}}), where (x\neq0), (y\neq0), and (x\neq y)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 43Expert MathematicsWhich option gives the simplified form of (\frac{x^{-1}+y^{-1}}{(xy)^{-1}}), where (x\neq0) and (y\neq0)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 45Hard MathematicsIf (a>0) and (b>0), what is the simplified form of (\sqrt{a^4b^2})?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 44Hard MathematicsIf (x \neq 0), what is the simplified form of (\dfrac{x^{-3}+x^{-2}}{x^{-3}})?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 44Hard MathematicsIf (a \neq 0) and (b \neq 0), what is the simplified form of (\dfrac{(a^{-2}b^3)^2}{(ab^{-1})^{-1}})?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 44Hard MathematicsIf (a>0) and (b>0), what is the simplified form of (\sqrt{a^2b^4})?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 43Hard MathematicsIf (a>0), what is the simplified form of (\dfrac{(a^{\frac{1}{2}}\times a^{\frac{3}{2}})^2}{a^3})?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 43Hard MathematicsIf (a \neq 0), what is the simplified form of (\dfrac{a^m \times a^{2m}}{a^{3m-2}})?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 43Hard MathematicsIf \(a\neq0\) and \(b\neq0\), what is the simplified form of \(\left(\frac{a^{-2}}{b^{-4}}\right)^{-1}\)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 45Medium MathematicsIf \(x\ne0\), what is the simplified form of \(\frac{x^7\cdot x^{-3}}{x^2}\)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 45Medium MathematicsIf \(x\ne0\) and \(y\ne0\), what is the simplified form of \(\left(\frac{x^{-3}}{y^{-2}}\right)^{-1}\)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 44Medium MathematicsIf \(x\neq0\) and \(y\neq0\), what is the simplified form of \(\frac{x^6y^{-3}}{x^3y^{-5}}\)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 44Medium MathematicsIf \(a\neq0\) and \(b\neq0\), what is the simplified form of \(\frac{24a^5b^3}{6a^2b^2}\)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 44Medium MathematicsIf \(x\neq0\), what is the simplified form of \(\frac{(3x^2)^2}{9x}\)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 44Medium MathematicsIf \(x\neq 0\), what is the simplified form of \(\frac{(x^2)^3\cdot x^{-1}}{x^2}\)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 44Medium MathematicsIf x ≠ 0, what is the simplest form of (x³ × x⁵) / x⁴?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 43Medium MathematicsIf \(x\neq0\) and \(y\neq0\), what is the simplified form of \(\left(\frac{x^{-2}}{y^{-3}}\right)^{-1}\)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 43Medium MathematicsWhat is the simplified form of \(\frac{x^5y^{-2}}{x^2y^{-4}}\), if \(x\neq0\) and \(y\neq0\)?Class 10PolynomialsOperations on real numbers and the laws of exponentsLevel 43Medium