Question 51

$x^{m} + x^{m} = x^{2 m},$ where $x$ is a non-zero rational number and $m$ is a positive integer.

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Solution

False
$∵ a^{m} \times a^{n} = a^{m + n} ∴ x^{m} \times x^{m} = x^{m + m} = x^{2 m} A l s o, a^{k} + a^{k} = 2 a^{k} S o, x^{m} + x^{m} = 2 x^{m}$

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Question 54

$x^{m} \times x^{n} = x^{m + n},$ where $x$ is a non-zero rational number and $m, n$ are positive integers.

Question 52

$x^{m} \times y^{m} = (x \times y)^{2 m},$ where $x$ and $y$ are non-zero rational numbers and $m$ is a positive integer.

$x^{m} \div y^{m} = (x \div y)^{m},$ where $x$ and $y$ are non-zero rational numbers and $m$ is a positive integer.

m

\int \frac{x^{5 m - 1} + 2. x^{4 m - 1}}{(x^{2 m} + x^{m} + 1)^{3}} d x = f (x) + c,

f (x)

\int \frac{x^{5 m - 1} + 2 x^{4 m - 1}}{(x^{2 m} + x^{m} + 1)^{3}} d x = f (x) + c

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