Find x- ifi 14-4 - 14-8-14-4 xii -12-19 x-128-12-2 x-1iii 32-3 - 325-322 x-1iv 25-3 - 2515-252-3 xv 54-x - 54-4-545vi 832 x -1 - 835-83 x -2

(i) We have: nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Byju's Answer

Standard VIII

Mathematics

Laws of Exponents

Find x, ifi 1...

Question

Find x, if
(i) ${(\frac{1}{4})}^{- 4} \times {(\frac{1}{4})}^{- 8} = {(\frac{1}{4})}^{- 4 x}$
(ii) ${(\frac{- 1}{2})}^{- 19} \times {(\frac{- 1}{2})}^{8} = {(\frac{- 1}{2})}^{- 2 x + 1}$
(iii) ${(\frac{3}{2})}^{- 3} \times {(\frac{3}{2})}^{5} = {(\frac{3}{2})}^{2 x + 1}$
(iv) ${(\frac{2}{5})}^{- 3} \times {(\frac{2}{5})}^{15} = {(\frac{2}{5})}^{2 + 3 x}$
(v) ${(\frac{5}{4})}^{- x} \div {(\frac{5}{4})}^{- 4} = {(\frac{5}{4})}^{5}$
(vi) ${(\frac{8}{3})}^{2 x + 1} \times {(\frac{8}{3})}^{5} = {(\frac{8}{3})}^{x + 2}$

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Solution

(i) We have:

$left(frac{1}{4} right )^{-4}timesleft(frac{1}{4} right )^{-8}&=&left(frac{1}{4} right )^{-4x}$
$left(frac{1}{4} right )^{-12}right )&=&left(frac{1}{4} right )^{-4x}$ $(a^{m} \times a^{n} = a^{m + n})$

x = 3

(ii) We have:

$left(frac{-1}{2} right )^{-19}timesleft(frac{-1}{2} right )^{8}=left(frac{-1}{2} right )^{-2x+1}$
$left(frac{-1}{2} right )^{-11}=left(frac{-1}{2} right )^{-2x+1}$ $(a^{m} \times a^{n} = a^{m + n})$

x = 6

(iii) We have:

$left(frac{3}{2} right )^{-3}timesleft(frac{3}{2} right )^{5}=left(frac{3}{2} right )^{2x+1}$
$left(frac{3}{2} right )^{2}=left(frac{3}{2} right )^{2x+1}$

$frac{1}{2}=x$
x = 1/2

(iv) We have:

$left(frac{2}{5} right )^{-3}timesleft(frac{2}{5} right )^{15}=left(frac{2}{5} right )^{2+3x}$
$left(frac{2}{5} right )^{12}=left(frac{2}{5} right )^{2+3x}$

$frac{10}{3}=x$
x = 10/3

(v) We have:

$left(frac{5}{4} right )^{-x}divleft(frac{5}{4} right )^{-4}=left(frac{5}{4} right )^{5}$
$left(frac{5}{4} right )^{-x+4}=left(frac{5}{4} right )^{5}$

x = −1

(vi) We have:

$left(frac{8}{3} right )^{2x+1}timesleft(frac{8}{3} right )^{5}=left(frac{8}{3} right )^{x+2}$
$left(frac{8}{3} right )^{2x+6}=left(frac{8}{3} right )^{x+2}$

x = −4

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Similar questions

Find x, if

$(i) {(\frac{1}{4})}^{- 4} \times {(\frac{1}{4})}^{- 8} = {(\frac{1}{4})}^{- 4 x} (i i) {(\frac{- 1}{2})}^{- 19} \div {(\frac{- 1}{2})}^{8} = {(\frac{- 1}{2})}^{- 2 x + 1} (i i i) {(\frac{3}{2})}^{- 3} \div {(\frac{3}{2})}^{5} = {(\frac{3}{2})}^{2 x + 1} (i v) {(\frac{2}{5})}^{- 3} \times {(\frac{2}{5})}^{15} = {(\frac{2}{5})}^{2 + 3 x} (v) {(\frac{5}{4})}^{- x} \div {(\frac{5}{4})}^{- 4} = {(\frac{5}{4})}^{5} (v i) {(\frac{8}{3})}^{2 x + 1} \times {(\frac{8}{3})}^{5} = {(\frac{8}{3})}^{x + 2}$