Simplify- i- 1-3 -3- 1-2 -3- 1-4 -3-ii 32-22 - 2-3 -3-iii- 1-2 - -4-1-1-iv- - -1-4 2 -2 -1-v- 2-3 2 3 - 1-3 -4- 3-1- 6 -1

(i) { ( 1/3 )^ 3 ( 1/2 )^ 3}÷ ( 1/4 )^ 3 =(3^3 2^3)÷ (4)^3 =(27 8)÷ 64=19/64 (ii) ( 3^2 2^2 )× ( 2/3 )^ 3 =(3^2 2^2)× ( 3/2 )^3=(9 4) ×27/8 =5 ×27/8=135/8 (i ...

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Byju's Answer

Standard VIII

Mathematics

Power of a Power

Simplify: i ...

Question

Simplify:

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

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Solution

$(i) {{(\frac{1}{3})}^{- 3} - {(\frac{1}{2})}^{- 3}} \div {(\frac{1}{4})}^{- 3} = (3^{3} - 2^{3}) \div (4)^{3} = (27 - 8) \div 64 = \frac{19}{64} (i i) (3^{2} - 2^{2}) \times {(\frac{2}{3})}^{- 3} = (3^{2} - 2^{2}) \times {(\frac{3}{2})}^{3} = (9 - 4) \times \frac{27}{8} = 5 \times \frac{27}{8} = \frac{135}{8} (i i i) {(\frac{1}{2}) \times (- 4)^{- 1}}^{- 1} = {(2)^{1} \times (\frac{1}{- 4})}^{- 1} = {(2 \times \frac{1}{- 4})}^{- 1} = {(\frac{- 1}{2})}^{- 1} = (- 2)^{1} = - 2 (i v) {[{{(\frac{- 1}{4})}^{2}}^{- 2}]}^{- 1} = {(\frac{- 1}{4})}^{2 \times (- 2) \times (- 2)} = {(\frac{- 1}{4})}^{4} = (\frac{- 1}{4}) \times (\frac{- 1}{4}) \times (\frac{- 1}{4}) \times (\frac{- 1}{4}) = \frac{1}{256} (v) {{(\frac{2}{3})}^{2}}^{3} \times {(\frac{1}{3})}^{- 4} \times 3^{- 1} \times 6^{- 1} = {(\frac{2}{3})}^{2 \times 3} \times {(\frac{3}{1})}^{4} \times \frac{1}{3^{1}} \times \frac{1}{6^{1}} = {(\frac{2}{3})}^{6} \times (3)^{4} \times \frac{1}{3} \times \frac{1}{6} = \frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{3 \times 3 \times 3 \times 3 \times 3 \times 3} \times 3 \times 3 \times 3 \times 3 \times \frac{1}{3} \times \frac{1}{6} = \frac{64}{3 \times 3 \times 3 \times 6} = \frac{64}{81 \times 2} = \frac{32}{81}$

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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}

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}

(v)

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

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}

Evaluate :

$(i) (3^{- 1} \times 9^{- 1}) \div 3^{- 2} (i i) (3^{- 1} \times 4^{- 1}) \div 6^{- 1} (i i i) (2^{- 1} + 3^{- 1})^{3} (i v) (3^{- 1} \div 4^{- 1})^{2} (v) (2^{2} + 3^{2}) \times {(\frac{1}{2})}^{2} (v i) (5^{2} - 3^{2}) \times {(\frac{2}{3})}^{- 3} (v i i) [{(\frac{1}{4})}^{- 3} - {(\frac{1}{3})}^{- 3}] \div {(\frac{1}{6})}^{- 3} (v i i i) {[{(- \frac{3}{4})}^{- 2}]}^{2} (i x) {{(\frac{3}{5})}^{- 2}}^{- 2} (x) (5^{- 1} \times 3^{- 1}) \div 6^{- 1}$

1 + 2 + 3 + 4 + . . . . . + n = ?

1 + 2 + 3 + 4 + . . . . . + (n - 1) = ?

1 + 1 + 1 + 1 + . . . . . + n = ?

1 + 1 + 1 + 1 + . . . . . . + (n - 1) = ?

1^{2} + 2^{2} + 3^{2} + 4^{2} + . . . . + n^{2} = ?

1^{2} + 2^{2} + 3^{2} + 4^{2} + . . . . + {(n - 1)}^{2} = ?

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Simplify: (i) {(13)−3−(12)−3}÷(14)−3 (ii)(32−22)×(23)−3(iii) {(12)×(−4)−1}−1 (iv) [{(−14)2}−2]−1(v) {(23)2}3×(13)−4×3−1×6−1