Evaluate - i-3-1-9-1-3-2- ii-3-1-4-1-6-1- iii-2-1-3-13- iv-3-1-4-12- v-22-32-1-2 2- vi-52-32-2-3 -3- vii-1-4 -3-1-3 -3 -1-6 -3- viii-3-4 -2 -2- ix-3-5-2-2- x-5-1-3-1-6-1

(i) (3^ 1×9^ 1)÷3^ 2 =(1/3×1/9 )÷1/3×1/3 =1/27÷1/9 =1/27×9/1=1/3 (ii) (3^ 1×4^ 1)÷6^ 1 =(1/3×1/4 )÷1/6 =1/12÷1/6 =1/12×6/1=1/2 (iii) (2^ 1+3^ 1)^3 =(1/2 ...

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Byju's Answer

Standard VIII

Mathematics

Exponents with like Bases

Evaluate : i ...

Question

Evaluate :

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

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Simplify:

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

Solve

(a) (b)

(e) (f)

(g) (h)

(i) (j)

(k) (l)

(m) (n)

Prove that :

$(i) (\sqrt{3 \times 5^{- 3}} \div \sqrt[3]{3^{- 1}} \sqrt{5}) \times \sqrt[6]{3 \times 5^{6}} = \frac{3}{5} (i i) 9^{\frac{3}{2}} - 3 \times 5^{0} - {(\frac{1}{81})}^{\frac{- 1}{2}} = 15 (i i i) {(\frac{1}{4})}^{- 2} - 3 \times 8^{\frac{2}{3}} \times 4^{0} + {(\frac{9}{16})}^{\frac{- 1}{2}} = \frac{16}{3} (i v) \frac{2^{\frac{1}{2}} \times 3^{\frac{1}{3}} \times 4^{\frac{1}{4}}}{10^{\frac{- 1}{5}} \times 5^{\frac{3}{5}}} \div \frac{3^{\frac{4}{3}} \times 5^{\frac{- 7}{5}}}{4^{\frac{- 3}{5}} \times 6} = 10 (v) \sqrt{\frac{1}{4}} + (0.01)^{\frac{- 1}{2}} - (27)^{\frac{2}{3}} = \frac{3}{2} (v i) \frac{2^{n} + 2^{n - 1}}{2^{n + 1} - 2^{n}} = \frac{3}{2} (v i i) {(\frac{64}{125})}^{\frac{- 2}{3}} + \frac{1}{{(\frac{256}{625})}^{\frac{1}{4}}} + {(\frac{\sqrt{25}}{\sqrt[3]{64}})}^{0} = \frac{61}{16} (v i i i) \frac{3^{- 3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{\frac{1}{25}} \times (15)^{\frac{- 4}{3}} \times 3^{\frac{1}{3}}} = 28 \sqrt{2} (i x) \frac{(0.6)^{0} - (0.1)^{- 1}}{{(\frac{3}{8})}^{- 1} {(\frac{3}{2})}^{3} + {(\frac{1}{3})}^{- 1}} = - \frac{3}{2}$

Q. Simplify:

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

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

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Evaluate : (i) (3−1×9−1)÷3−2(ii) (3−1×4−1)÷6−1(iii) (2−1+3−1)3(iv) (3−1÷4−1)2(v) (22+32)×(12)2(vi) (52−32)×(23)−3(vii) [(14)−3−(13)−3]÷(16)−3(viii) [(−34)−2]2(ix) {(35)−2}−2(x) (5−1×3−1)÷6−1