Simplify (4×10^7 × 6×10^-5) / (8×10^4) Simplify: \(\frac{(4\times10^7)(6\times10^{-5})}{8\times10^4}\) Solution \[ = \frac{24 \times 10^{2}}{8 \times 10^{4}} \] \[ = 3 \times 10^{-2} \] Final Answer: \[ \boxed{3 \times 10^{-2}} \] Next Question / Full Exercise
Simplify: ((4×10^7) (6×10^-5))/{8×10^4} Read More »
Simplify (2x^-2y^3)^3 Simplify: \((2x^{-2}y^3)^3\) Solution \[ = 2^3 \cdot x^{-6} \cdot y^{9} \] \[ = \frac{8y^9}{x^6} \] Final Answer: \[ \boxed{\frac{8y^9}{x^6}} \] Next Question / Full Exercise
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Assertion Reason MCQ on Decimal Expansion Question Statement-1 (Assertion): The decimal representation of \( \frac{3}{8} \) is terminating. Statement-2 (Reason): If the denominator of a rational number is of the form \(2^m \times 5^n\), where \(m, n\) are non-negative integers, then its decimal representation is terminating. Options: (a) Statement-1 is true, Statement-2 is true; Statement-2
Simplify 3(a^4b^3)^10 × 5(a^2b^2)^3 Simplify: \(3(a^4b^3)^{10} \times 5(a^2b^2)^3\) Solution \[ = 3 \times 5 \cdot a^{40}b^{30} \cdot a^{6}b^{6} \] \[ = 15 \cdot a^{46}b^{36} \] Final Answer: \[ \boxed{15a^{46}b^{36}} \] Next Question / Full Exercise
Simplify : 3(a^4b^3)^10 ×5(a^2b^2)^3 Read More »
Assertion Reason MCQ on Rational Numbers Question Statement-1 (Assertion): There are two rational numbers whose sum and product both are rationals. Statement-2 (Reason): There are numbers which cannot be written in the form \( \frac{p}{q} \), \( q \neq 0 \), where \( p, q \) are integers. Options: (a) Statement-1 is true, Statement-2 is
Assertion Reason MCQ on √2 and Number Properties Question Statement-1 (Assertion): \( \sqrt{2} \) is an irrational number. Statement-2 (Reason): The sum of a rational number and an irrational number is an irrational number. Options: (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2 is
Assertion Reason MCQ on √3 Irrational Question Statement-1 (Assertion): \( \sqrt{3} \) is an irrational number. Statement-2 (Reason): The square root of a positive integer which is not a perfect square is an irrational number. Options: (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2
Assertion Reason MCQ on Irrational Numbers Product Question Statement-1 (Assertion): The product of any two irrational numbers is an irrational number. Statement-2 (Reason): There are two irrational numbers whose product is not an irrational number. Options: (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2
Assertion Reason MCQ on Irrational Numbers Question Statement-1 (Assertion): The sum of any two irrational numbers is an irrational number. Statement-2 (Reason): There are two irrational numbers whose sum is a rational number. Options: (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2 is true;
Assertion Reason MCQ on √2 Irrational Question Statement-1 (Assertion): \( \sqrt{2} \) is an irrational number. Statement-2 (Reason): The decimal expansion of \( \sqrt{2} \) is non-terminating and non-recurring. Options: (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2 is true; Statement-2 is not a