Simplify-i 4-1 - 3-12ii 5-1 - 6-13iii 2-1-3-1-1iv 3-1 - 4-1-1 - 5-1v 4-1-5-1 - 3-1

nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; — gt; (a−1 = 1/a) nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VI

Mathematics

Integers

Simplify:i 4-...

Question

Simplify:
(i) ${\{4^{- 1} \times 3^{- 1}\}}^{2}$
(ii) ${\{5^{- 1} \div 6^{- 1}\}}^{3}$
(iii) ${(2^{- 1} + 3^{- 1})}^{- 1}$
(iv) ${\{3^{- 1} \times 4^{- 1}\}}^{- 1} \times 5^{- 1}$
(v) $(4^{- 1} - 5^{- 1}) \div 3^{- 1}$

Open in App

Solution

$(i)left(4^{-1}times3^{-1} right )^2=left(frac{1}{4}times frac{1}{3}right )^2$ ---> (a⁻¹ = 1/a)
$= {(\frac{1}{12})}^{2}$
$= \frac{(1)^{2}}{(12)^{2}}$ --->((a/b)ⁿ = (aⁿ)/(bⁿ))
$= \frac{1}{144}$

$(ii)left(5^{-1}div6^{-1} right )^3=left(frac{1}{5}divfrac{1}{6} right)^3$ ---> (a⁻¹ = 1/a)
$= {(\frac{6}{5})}^{3}$
$= \frac{216}{125}$ --->((a/b)ⁿ = (aⁿ)/(bⁿ))

$(i i i) {(2^{- 1} + 3^{- 1})}^{- 1} = {(\frac{1}{2} + \frac{1}{3})}^{- 1} {---> (a}^{- 1} = 1/a) = {(\frac{5}{6})}^{- 1} = \frac{6}{5} {---> (a}^{- 1} = 1/a)$

$(iv)left(3^{-1}times4^{-1} right )^{-1}times5^{-1}=left(frac{1}{3}timesfrac{1}{4} right )^{-1}timesfrac{1}{5}$ ---> (a⁻¹ = 1/a)
$= {(\frac{1}{12})}^{- 1} \times \frac{1}{5}$
$= 12 \times \frac{1}{5}$ ---> (a⁻¹ = 1/a)
$= \frac{12}{5}$

$(v)left(4^{-1}-5^{-1} right )div 3^{-1}=left(frac{1}{4}-frac{1}{5} right )div frac{1}{3}$ ---> (a⁻¹ = 1/a)
$=left(frac{5-4}{20} right )times 3$
$= \frac{1}{20} \times 3$

$= \frac{3}{20}$

Suggest Corrections

Similar questions

Q. Simplify:
(i)

{(4^{- 1} \times 3^{- 1})}^{2}

(ii)

{(5^{- 1} \div 6^{- 1})}^{3}

(iii)

{(2^{- 1} + 3^{- 1})}^{- 1}

(iv)

{(3^{- 1} \times 4^{- 1})}^{- 1} \times 5^{- 1}

Simplify:

$(i) {{(\frac{1}{3})}^{- 3} - {(\frac{1}{2})}^{- 3}} \div {(\frac{1}{4})}^{- 3} (i i) (3^{2} - 2^{2}) \times {(\frac{2}{3})}^{- 3} (i i i) {(\frac{1}{2}) \times (- 4)^{- 1}}^{- 1} (i v) {[{{(\frac{- 1}{4})}^{2}}^{- 2}]}^{- 1} (v) {{(\frac{2}{3})}^{2}}^{3} \times {(\frac{1}{3})}^{- 4} \times 3^{- 1} \times 6^{- 1}$

Q. Simplify:
(i)

\{{(\frac{1}{3})}^{- 3} - {(\frac{1}{2})}^{- 3}\} \div {(\frac{1}{4})}^{- 3}

(ii)

(3^{2} - 2^{2}) \times {(\frac{2}{3})}^{- 3}

(iii)

{\{{(\frac{1}{2})}^{- 1} \times (- 4)^{- 1}\}}^{- 1}

(iv)

{[{\{{(\frac{- 1}{4})}^{2}\}}^{- 2}]}^{- 1}

(v)

{\{{(\frac{2}{3})}^{2}\}}^{3} \times {(\frac{1}{3})}^{- 4} \times 3^{- 1} \times 6^{- 1}

Find the mode from the given data.

1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2 , 3, 4, 1, 2, 3, 4, 1 ,2 , 3, 4, 5, 5, 1, 5, 5, 5, 3, 5, 1, 2, 4, 5, 6, 1, 2, 4, 2, 1

Find x, if

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

Join BYJU'S Learning Program

Simplify: (i) 4-1×3-12 (ii) 5-1÷6-13 (iii) 2-1+3-1-1 (iv) 3-1×4-1-1×5-1 (v) 4-1-5-1÷3-1

---> (a−1 = 1/a) =1122 =(1)2(12)2 --->((a/b)n = (an)/(bn)) =1144 ---> (a−1 = 1/a) =653 =216125 --->((a/b)n = (an)/(bn)) (iii) 2-1 + 3-1-1 = 12+ 13-1 ---> (a-1= 1/a) = 56-1 = 65 ---> (a-1= 1/a) ---> (a−1 = 1/a) =112-1×15 =12×15 ---> (a−1 = 1/a) =125 ---> (a−1 = 1/a) =120×3 =320

Simplify:
(i) ${\{4^{- 1} \times 3^{- 1}\}}^{2}$
(ii) ${\{5^{- 1} \div 6^{- 1}\}}^{3}$
(iii) ${(2^{- 1} + 3^{- 1})}^{- 1}$
(iv) ${\{3^{- 1} \times 4^{- 1}\}}^{- 1} \times 5^{- 1}$
(v) $(4^{- 1} - 5^{- 1}) \div 3^{- 1}$