Prove that 93-2-3-50-1-81-1-2-15-

Simplify the expression using the law of radical exponent.9^3/2 3×5^0 (1/81)^ 1/2=15Taking LCM[ =9^3/2 3×5^0 (1/81)^ 1/2; ...

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Byju's Answer

Standard VII

Mathematics

Powers with Negative Exponents

Prove that 93...

Question

Prove that $9^{3 / 2} - 3 \times 5^{0} - {(\frac{1}{81})}^{- 1 / 2} = 15$ .

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Solution

Simplify the expression using the law of radical exponent.
$9^{3 / 2} - 3 \times 5^{0} - {(\frac{1}{81})}^{- 1 / 2} = 15$
Taking $LCM$
$\begin{array}{l} = 9^{3 / 2} - 3 \times 5^{0} - {(\frac{1}{81})}^{- 1 / 2} \\ = {(3^{2})}^{\frac{3}{2}} - 3 \times 5^{0} - {(\frac{1}{9^{2}})}^{- 1 / 2} \\ = {(3^{2})}^{\frac{3}{2}} - 3 \times 5^{0} - {(9^{- 2})}^{- \frac{1}{2}} [∵ p^{- n} = \frac{1}{p^{n}}] \\ = {(3)}^{2 \times \frac{3}{2}} - 3 \times 5^{0} - {(9)}^{- 2 \times - \frac{1}{2}} [∵ {(p^{m})}^{n} = p^{m \times n}] \\ = {(3)}^{3} - 3 \times 5^{0} - {(9)}^{1} \\ = 27 - 3 - 9 \\ = 15 = RHS \end{array}$
Hence, it is been proved that $9^{3 / 2} - 3 \times 5^{0} - {(\frac{1}{81})}^{- 1 / 2} = 15$ .

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Prove that :

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

From the given place value table, write the decimal number.

Thousands	Hundreds	Tens	Ones	Tenths	Hundredths	Thousandths
$(1000)$	$(100)$	$(10)$	$(1)$	$(\frac{1}{10})$	$(\frac{1}{100})$	$(\frac{1}{1000})$
				$8$	$2$	$3$

Q. Prove that :

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

Q. Show that:

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

Find the value of 9^3/2-3 x 5⁰- (1/18)^-1/2

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Prove that 93/2−3×50−181−1/2=15.

Prove that $9^{3 / 2} - 3 \times 5^{0} - {(\frac{1}{81})}^{- 1 / 2} = 15$ .