Question 11 Mark$5^0 \times 25^0 \times 125^0=\left(5^0\right)^6$AnswerTrueView full question & answer→
Question 31 Mark$x^0 \times x^0=x^0 \div x^0$ is true for all non-zero values of $x$.AnswerTrueView full question & answer→
Question 51 Mark$\left(\frac{2}{5}\right)^3 \div\left(\frac{5}{2}\right)^3=1$AnswerFalseView full question & answer→
Question 61 MarkSay true or false and Justify your answer.$3^0=(1000)^0$Answer$\operatorname{True}, 3^0=(1000)^0$JustificationLHS $=3^0=1 \quad[$ since, number (except 0 raised to the power (exponent) 0 is 1$]$RHS $=(1000)^0=1$$\because \quad 1=1$$\therefore \quad$ LHS $=$ RHSTherefore, $3^0=(1000)^0$View full question & answer→
Question 71 MarkSay true or false and Justify your answer.$2^3 \times 3^2=6^5$AnswerFalse, $2^3 \times 3^2 \neq 6^5$ Justification$\begin{array}{l}\text { LHS }=2^3 \times 3^2=(2 \times 2 \times 2) \times(3 \times 3)=8 \times 9=72 \\ \text { RHS }=6^5=6 \times 6 \times 6 \times 6 \times 6=7776\end{array}$$\begin{array}{l}\because \quad 72 \neq 7776, \text { so LHS } \neq \text { RHS } \\ \text { Therefore, } 2^3 \times 3^2 \neq 6^5\end{array}$View full question & answer→
Question 81 MarkSay true or false and Justify your answer.$2^3>5^2$AnswerFalse, $2^3>5^2$Justification$\begin{array}{l} LHS =2^3=2 \times 2 \times 2=8 \\ RHS =5^2=5 \times 5=25\end{array}$Since, $8<25,2^3<5^2$, so LHS $<$ RHSTherefore, $2^3 \ngtr 5^2$View full question & answer→
Question 91 MarkSay true or false and Justify your answer.$10 \times 10^{11}=100^{11}$AnswerFalse, $10 \times 10^{11} \neq 100^{11}$JustificationLHS $=10 \times 10^{11}=10^{1+11}=10^{12} \quad\left[\because a^m \times a^n=a^{m+n}\right]$RHS $=(100)^{11}=\left(10^2\right)^{11} \quad\left[\because 100=10 \times 10=10^2\right]$$=10^{2 \times 11}=10^{22} \quad\left[\because\left(a^m\right)^n=a^{m n}\right]$$\because \quad 10^{12} \neq 10^{22}$, so LHS $\neq$ RHSTherefore, $10 \times 10^{11} \neq 100^{11}$View full question & answer→