Simplify-i 32-22 - 123ii 32-22 - 23-3iii 13-3-12-3 - 14-3iv 22-32-42 - 322

(i) (32+22)×123=(9+4)×18=138 (ii) nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; — gt; (a−1=1/(an)) nbs ...

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Byju's Answer

Standard VIII

Mathematics

Division of Negative Numbers

Simplify:i 32...

Question

Simplify:
(i) $(3^{2} + 2^{2}) \times {(\frac{1}{2})}^{3}$
(ii) $(3^{2} - 2^{2}) \times {(\frac{2}{3})}^{- 3}$
(iii) $[{(\frac{1}{3})}^{- 3} - {(\frac{1}{2})}^{- 3}] \div {(\frac{1}{4})}^{- 3}$
(iv) $(2^{2} + 3^{2} - 4^{2}) \div {(\frac{3}{2})}^{2}$

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Solution

(i)
$(3^{2} + 2^{2}) \times {(\frac{1}{2})}^{3} = (9 + 4) \times \frac{1}{8} = \frac{13}{8}$

(ii)
$left ( 3^2-2^2 right )times left(frac{2}{3} right )^{-3}=left(9-4 right )times frac{1}{left (2/3 right )^{3}}$ ---> (a⁻¹=1/(aⁿ))
$=5times frac{1}{8/27}$ ---> ((a/b)ⁿ = (aⁿ)/(bⁿ))
$= 5 \times \frac{27}{8}$
$= \frac{135}{8}$

(iii)
$left( left(frac{1}{3} right )^{-3}-left(frac{1}{2} right )^{-3}right )div left( frac{1}{4}right )^{-3}=left(3^3-2^3 right )div 4^3$ --->(a^-n = 1/(aⁿ))
= $(27 - 8) \div 64$
$= 19 \times \frac{1}{64}$
$= \frac{19}{64}$

(iv)
$(2^{2} + 3^{2} - 4^{2}) \div {(\frac{3}{2})}^{2} = (4 + 9 - 16) \times \frac{9}{4}$ ---> ((a/b)ⁿ = (aⁿ)/(bⁿ))

$= - 3 \times \frac{9}{4}$
$= \frac{- 27}{4}$

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Similar questions

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}

\frac{3}{1^{2} \times 2^{2}} - \frac{5}{2^{2} \times 3^{2}} + \frac{7}{3^{2} \times 4^{2}} +

.................

Q. 3, 2, 8, 9, 13, 22, 18, 32, 23, 42

\frac{1^{3} + 2^{3} + 3^{3} + 4^{3} + . . . . . . . {.12}^{3}}{1^{2} + 2^{2} + 3^{2} + 4^{2} + . . . . . {.12}^{2}} =

$1 + \frac{1^{2} + 2^{2}}{2!} + \frac{1^{2} + 2^{2} + 3^{2}}{3!} + \frac{1^{2} + 2^{2} + 3^{2} + 4^{2}}{4!} + . . . \infty = \frac{b}{6} e$ . Find $b$

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Simplify: (i) 32+22×123 (ii) 32-22×23-3 (iii) 13-3-12-3÷14-3 (iv) 22+32-42÷322

(i) (32+22)×123=(9+4)×18=138 (ii) ---> (a−1=1/(an)) ---> ((a/b)n = (an)/(bn)) =5×278 =1358 (iii) --->(a-n = 1/(an)) = (27-8)÷64 =19×164 =1964 (iv) (22+32-42)÷322=(4+9-16)×94 ---> ((a/b)n = (an)/(bn)) =-3×94 =-274

Simplify:
(i) $(3^{2} + 2^{2}) \times {(\frac{1}{2})}^{3}$
(ii) $(3^{2} - 2^{2}) \times {(\frac{2}{3})}^{- 3}$
(iii) $[{(\frac{1}{3})}^{- 3} - {(\frac{1}{2})}^{- 3}] \div {(\frac{1}{4})}^{- 3}$
(iv) $(2^{2} + 3^{2} - 4^{2}) \div {(\frac{3}{2})}^{2}$