TRUE / FALSE

Question 11 Mark

$\left(\frac{4}{3}\right)^5 \times\left(\frac{5}{7}\right)^5=\left(\frac{4}{3}+\frac{5}{7}\right)^5$

Answer

$\left(\frac{4}{3}\right)^5 \times\left(\frac{5}{7}\right)^5=\left(\frac{4}{3}+\frac{5}{7}\right)^5$ (False)
Correct :
$\left(\frac{4}{3}\right)^5 \times\left(\frac{5}{7}\right)^5 \neq\left(\frac{4}{3}+\frac{5}{7}\right)^5$

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Question 21 Mark

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

Answer

$x^{m!}+x^m=x^{2 m} \quad$ (False)
Correct : As $x^m+x^m=2 \times x^m$ and $x^{2 m}=\left(x^2\right)^m$

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Question 31 Mark

$4^9$ is greater than $16^3$.

Answer

$4^9$ is greater than $16^3$. $\text{(True)}$
$4^9$ and $16^3=\left(4^2\right)^3=4^6$
$\therefore 4^9>4^6$

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Question 41 Mark

$x^0 \times x^0=x^0 \div x^0$, where $x$ is a non$-$zero rational number.

Answer

$x^0 \times x^0=x^0 \div x^0 ($True $)$
$1 \times 1=1 \div 1$
$\Rightarrow 1=1$

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Question 51 Mark

$(10+10)^4=10^4+10^4$.

Answer

$(10+10)^4=10^4+10^4.\ \ \text{(False)}$
Correct :
$\because(10+10)^4=20^4 \text { but } 10^4+10^4=2 \times 10^4$

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Question 61 Mark

$\frac{2^3}{7}<\left(\frac{2}{7}\right)^3$

Answer

$\frac{2^3}{7}<\left(\frac{2}{7}\right)^3\ \ \text{(False)}$
Correct :
$\frac{8}{7}<\frac{8}{343} \quad\left(\because \frac{8}{7}>\frac{8}{343}\right)$

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Question 71 Mark

$5^0 \times 3^0=8^0$

Answer

$5^0 \times 3^0=8^0\ \ \text{(True)}$
$1 \times 1=1$
$\left\{5^0=1,3^0=1,8^0\right\}$

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Question 81 Mark

$5^6 \div(-2)^6=\frac{-5}{2}$

Answer

$5^6 \div(-2)^6=-\frac{5}{2}\ \ \text{(False)}$
$5^6 \div(-2)^6$
$=\frac{5^6}{(-2)^6}$
$=\left(\frac{5}{-2}\right)^6$

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Question 91 Mark

$3^0=(1000)^0$.

Answer

$3^0=(1000)^0.\ \text{(True)}$
$\left\{\right.$ As $3^0=1$ and $\left.(1000)^0=1\right\}$

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Question 101 Mark

The value of the expression $2^9 \times 2^{91}-2^{19} \times 2^{81}$ is 1.

Answer

The value of the expression $2^9 \times 2^{91}-2^{19} \times$ $2^{81}$ is 1. (False)
Correct :
$2^{9+91}-2^{19+81} \Rightarrow 2^{100}-2^{100}=0$

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Question 111 Mark

The value of $(-2)^{-3}$ is $\frac{-1}{8}$.

Answer

The value of $(-2)^{-3}$ is $-\frac{1}{8}$. (True)
$(-2)^{-3}==\frac{1}{(-2)^3}=\frac{1}{-8}=-\frac{1}{8}$

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Question 121 Mark

$2^3 \times 3^2=6^5$.

Answer

$2^3 \times 3^2=6^5\ \text{(False)}$
Correct : $\left\{\because 2^3 \times 3^2 \neq 6^5\right\}$

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Question 131 Mark

If $a$ is a rational number then $a^m \times a^n=a^{m \times n}$

Answer

If $a$ is a rational number then
$d^m \times d^n=d^{m \times n}.\ \text{(False)}$
Correct :
$\{\because$ It is true for fraction $\}$
$a^m \times a^n=a^{m+n}$

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