Find the value of 0-60-0-1-1322-1323-13-1

On solving the given expression, (0.6)^0 (0.1)^ 1(32^2)^ 1(32)^3+( 13)^ 1 we get 1 10.1(32^3)^ 1(32)^3+( 13)^ 1 because X^0=1 and (ab)^ n=(ba)^n 1 10(2^33)^1(3 ...

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Byju's Answer

Standard XII

Mathematics

Fundamental Laws of Logarithms

Find the valu...

Question

Find the value of $\frac{(0.6)^{0} - (0.1)^{- 1}}{(\frac{3}{2^{2}})^{- 1} (\frac{3}{2})^{3} + (\frac{- 1}{3})^{- 1}}$

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Solution

On solving the given expression,
$\frac{(0.6)^{0} - (0.1)^{- 1}}{(\frac{3}{2^{2}})^{- 1} (\frac{3}{2})^{3} + (\frac{- 1}{3})^{- 1}}$
we get
$\frac{1 - \frac{1}{0.1}}{(\frac{3}{2^{3}})^{- 1} (\frac{3}{2})^{3} + (\frac{- 1}{3})^{- 1}} b e c a u s e X^{0} = 1 a n d (\frac{a}{b})^{- n} = (\frac{b}{a})^{n} \frac{1 - 10}{(\frac{2^{3}}{3})^{1} (\frac{3}{2})^{3} + (\frac{3}{- 1})^{1}} = \frac{- 9}{3^{2} + (- 3)} = \frac{- 9}{9 + (- 3)} = \frac{- 9}{6} = \frac{- 3}{2}$

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Similar questions

Q. The value of

\frac{(0.6)^{0} - (0.1)^{- 1}}{(\frac{3}{2^{3}})^{- 1} (\frac{3}{2})^{3} + (- \frac{1}{3})^{- 1}}

is _____________.

Q. The value of

\frac{(0.6)^{0} - (0.1)^{1}}{{(\frac{3}{2^{3}})}^{- 1} {(\frac{3}{2})}^{3} + {(\frac{- 1}{3})}^{- 1}}

Q. Show that:

\frac{{(0.6)}^{0} - {(0.1)}^{- 1}}{{(\frac{3}{8})}^{- 1} {(\frac{3}{2})}^{3} + {(- \frac{1}{3})}^{- 1}} = - \frac{3}{2}

Q. Represent the following mixed infinite decimal periodic fractions as common fractions:

\frac{(0. 6)^{0} - (0.1)^{- 1}}{{(\frac{3}{2^{3}})}^{- 1} \cdot {(\frac{3}{2})}^{3} + {(- \frac{1}{3})}^{- 1}}

Q. Find the sum to

n

terms of the series:

\frac{1^{3}}{1} + \frac{1^{3} + 2^{2}}{2} + \frac{1^{3} + 2^{3} + 3^{3}}{3} + . . . . .

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Find the value of (0.6)0−(0.1)−1(322)−1(32)3+(−13)−1

On solving the given expression, (0.6)0−(0.1)−1(322)−1(32)3+(−13)−1 we get 1−10.1(323)−1(32)3+(−13)−1because X0=1 and (ab)−n=(ba)n1−10(233)1(32)3+(3−1)1=−932+(−3)=−99+(−3)=−96=−32

Find the value of $\frac{(0.6)^{0} - (0.1)^{- 1}}{(\frac{3}{2^{2}})^{- 1} (\frac{3}{2})^{3} + (\frac{- 1}{3})^{- 1}}$