Show that- 93-2-3- 5o-181-1-2-15

.H.S =9^3/2 3×5^0 (181)^ 1/2 =(3^2)^3/2 3×1 (13^4)^ 1/2 since a^0=1 =3^3 3 (3^ 4)^ 1/2 since (a^m)^n=a^mn =27 3 3^2=27 3 9=27 12= ...

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Standard IX

Mathematics

Mathematical Statements

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Question

Show that:
$9^{3 / 2} - 3 \times 5^{o} - {(\frac{1}{81})}^{- 1 / 2} = 15$

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Solution

.H.S $= 9^{\frac{3}{2}} - 3 \times 5^{0} - {(\frac{1}{81})}^{\frac{- 1}{2}}$
$= {(3^{2})}^{\frac{3}{2}} - 3 \times 1 - {(\frac{1}{3^{4}})}^{\frac{- 1}{2}}$ since $a^{0} = 1$
$= 3^{3} - 3 - {(3^{- 4})}^{\frac{- 1}{2}}$ since ${(a^{m})}^{n} = a^{m n}$
$= 27 - 3 - 3^{2} = 27 - 3 - 9 = 27 - 12 = 15 =$ R.H.S

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Similar questions

Q. Prove that :

9^{\frac{3}{2}} - 3 \times 2^{\circ} - {(\frac{1}{81})}^{\frac{1}{2}} = 15

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. Evaluate:

{(\frac{16}{81})}^{- \frac{3}{4}} \times {(\frac{49}{9})}^{\frac{3}{2}} \div {(\frac{343}{216})}^{\frac{2}{3}}

Q. Evaluate

{(\frac{16}{81})}^{- \frac{3}{4}} \times {(\frac{49}{9})}^{\frac{3}{2}} + {(\frac{343}{216})}^{\frac{2}{3}}

Q. Show that

\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}} = 1

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Show that: 93/2−3×5o−(181)−1/2=15

.H.S=932−3×50−(181)−12=(32)32−3×1−(134)−12 since a0=1=33−3−(3−4)−12 since (am)n=amn=27−3−32=27−3−9=27−12=15=R.H.S

Show that:
$9^{3 / 2} - 3 \times 5^{o} - {(\frac{1}{81})}^{- 1 / 2} = 15$