Question 12 MarksSimplify : $\frac{(27)^{\frac{2 n}{3}} \times(8)^{-\frac{n}{6}}}{(18)^{-\frac{n}{2}}}$Answer$3^{3 n}$View full question & answer→
Question 22 MarksSimplify : $\frac{3^n \times 9^{n+1}}{3^{n-1} \times 9^{n-1}}$Answer$3^5$View full question & answer→
Question 32 MarksIf $2^x=3^y=6^{-z}$, show that : $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$.AnswerselfView full question & answer→
Question 42 MarksIf $2^x=3^y=12^z$, show that : $\frac{1}{z}=\frac{1}{y}+\frac{2}{x}$.AnswerHint. Let $2^x=3^y=12^z=k$. Then, $2=k^{\frac{1}{x}}, 3=k^{\frac{1}{y}}$ and $12=k^{\frac{1}{x}}$.Now, $12=2^2 \times 3 \Rightarrow k^{\frac{1}{x}}=\left(k^{\frac{1}{x}}\right)^2 \times\left(k^{\frac{1}{y}}\right) \Rightarrow k^{\frac{1}{x}}=k^{\left(\frac{2}{x}+\frac{1}{y}\right)}$View full question & answer→
Question 52 MarksSolve for n : \[\left(3^n \times 9^{n+1}\right) \div\left(3^{n-1} \times 27^{n-1}\right)=81\]Answer$n=2$View full question & answer→
Question 72 MarksSolve for x: $2^{(5 x-1)}=4 \times 2^{(3 x+1)}$Answer$x=2$View full question & answer→
Question 82 MarksSolve for x: $9 \times 3^x=(27)^{2 x-5}$Answer$x=3 \frac{2}{5}$View full question & answer→
Question 92 MarksSolve for x: $\left(\sqrt{\frac{3}{5}}\right)^{x-1}=\left(\frac{27}{125}\right)^{-1}$Answer$x=-5$View full question & answer→
Question 102 MarksSolve for x: $\left(\sqrt[3]{\frac{2}{3}}\right)^{x-1}=\frac{27}{8}$Answer$x=-8$View full question & answer→
Question 112 MarksSolve for x: $\sqrt{\frac{a}{b}}=\left(\frac{b}{a}\right)^{1-3 x}$Answer$x=\frac{1}{2}$View full question & answer→
Question 162 MarksEvaluate : $\left(\frac{8}{125}\right)^{-\frac{1}{3}}$Answer$\frac{5}{2}$View full question & answer→
Question 182 MarksEvaluate : $(0.027)^{\frac{-2}{3}}$Answer$\frac{100}{9}$View full question & answer→
Question 232 MarksSimplify : $\frac{a+b+c}{\left(a^{-1} b^{-1}+b^{-1} c^{-1}+c^{-1} a^{-1}\right)}$Answer$a b c$View full question & answer→
Question 242 MarksSimplify : $(a+b)^{-1} \times\left(a^{-1}+b^{-1}\right)$Answer$\frac{1}{a b}$View full question & answer→
Question 252 MarksSimplify : $\left(a^{-1} \times b^{-1}\right) \div\left(a^{-1}+b^{-1}\right)$Answer$\frac{1}{(a+b)}$View full question & answer→
Question 262 MarksSimplify : $\left(a^{-1}+b^{-1}\right) \div(a b)^{-1}$Answer$(a+b)$View full question & answer→
Question 272 MarksSimplify : $\left(a^{-1}+b^{-1}\right) \div\left(a^{-2}-b^{-2}\right)$Answer$\frac{a b}{(b-a)}$View full question & answer→
Question 282 MarksSimplify : $a^{\frac{4}{3}} \div a^{-\frac{2}{3}}$Answer$a^2$View full question & answer→
Question 292 MarksSimplify : $a^7 \times a^4 \times a^{-6} \times a^0$Answer$a^5$View full question & answer→
Question 302 MarksSimplify : $\left(x^{\frac{1}{3}}-x^{-\frac{1}{3}}\right)\left(x^{2 / 3}+1+x^{-2 / 3}\right)$Answer$\left(x-\frac{1}{x}\right)$$\begin{aligned}\text { [Hint. Given Exp. }& =(a-b)\left(a^2+a b+b^2\right) \\ & \left.=\left(a^3-b^3\right)\right]\end{aligned}$View full question & answer→
Question 312 MarksSimplify : $\frac{7^{(2 n+3)}-(49)^{n+2}}{\left[(343)^{n+1}\right]^{\frac{2}{3}}}$Answer-42View full question & answer→
Question 322 MarksSimplify : $\frac{5 \times(25)^{n+1}-25 \times 5^{2 n}}{5 \times 5^{(2 n+3)}-(25)^{n+1}}$Answer$\frac{1}{6}$View full question & answer→
Question 332 MarksSimplify : $\frac{3 \times(27)^{n+1}+9 \times 3^{(3 n-1)}}{8 \times 3^{3 n}-5 \times(27)^n}$Answer28View full question & answer→
Question 342 MarksSimplify : $\frac{5^{n+3}-16 \times 5^{n+1}}{12 \times 5^n-2 \times 5^{n+1}}$Answer22.5View full question & answer→
Question 352 MarksSimplify : $\frac{5^{2(n+6)} \times(25)^{-7+2 n}}{(125)^{2 n}}$Answer$\frac{1}{25}$View full question & answer→
Question 362 MarksIf $(x-1)^{1 / 2}+(y-2)^{1 / 2}+(z-3)^{1 / 2}=0$, then find the values of $x, y$ and $z$.Answer1, 2, 3View full question & answer→
Question 372 MarksIf you raise a number to a negative power, can the resulting number be greater than the original number. Justify your answer by giving suitable examples.AnswerYes, if the base is a fraction between o and 1.View full question & answer→
Question 392 MarksSolve for x:$2^{(5 x-1)}=4 \times 2^{(3 x+1)}$Answerx = 2View full question & answer→
Question 402 MarksSolve for x:$9 \times 3^x=(27)^{2 x-5}$Answer$x=3 \frac{2}{5}$View full question & answer→
Question 412 MarksSolve for x:$\left(\sqrt{\frac{3}{5}}\right)^{x-1}=\left(\frac{27}{125}\right)^{-1}$Answerx = -5View full question & answer→
Question 422 MarksSolve for x:$\left(\sqrt[3]{\frac{2}{3}}\right)^{x-1}=\frac{27}{8}$Answerx = -8View full question & answer→
Question 432 MarksSolve for x:$\sqrt{\frac{a}{b}}=\left(\frac{b}{a}\right)^{1-3 x}$Answer$x=\frac{1}{2}$View full question & answer→
Question 462 MarksSimplify:$\frac{a+b+c}{\left(a^{-1} b^{-1}+b^{-1} c^{-1}+c^{-1} a^{-1}\right)}$AnswerabcView full question & answer→
Question 472 MarksSimplify:$(a+b)^{-1} \times\left(a^{-1}+b^{-1}\right)$Answer$\frac{1}{a b}$View full question & answer→
Question 482 MarksSimplify:$\left(a^{-1} \times b^{-1}\right) \div\left(a^{-1}+b^{-1}\right)$Answer$\frac{1}{(a+b)}$View full question & answer→
Question 492 MarksSimplify:$\left(a^{-1}+b^{-1}\right) \div(a b)^{-1}$Answer(a + b)View full question & answer→
Question 502 MarksSimplify:$\left(a^{-1}+b^{-1}\right) \div\left(a^{-2}-b^{-2}\right)$Answer$\frac{a b}{(b-a)}$View full question & answer→