Evaluate- 90-9-1-9-2-91-2-9-1-2

nbsp; amp;9^0+9^ 1 9^ 2+9^1/2 9^ 1/2 amp;=1+1/9 1/9^2+(3^2)^1/2 (3^2)^ 1/2 amp;=1+1/9 1/81+3^2 ×1/2 3^2 ×( 1/2) amp;=1+1/9 1/81 ...

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Byju's Answer

Standard VIII

Mathematics

Exponents with Unlike Bases and Same Exponent

Evaluate: 90...

Question

Evaluate:
$9^{0} + 9^{- 1} - 9^{- 2} + 9^{\frac{1}{2}} - 9^{- \frac{1}{2}}$

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Solution

$\begin{matrix} 9^{0} + 9^{- 1} - 9^{- 2} + 9^{\frac{1}{2}} - 9^{- \frac{1}{2}} = 1 + \frac{1}{9} - \frac{1}{9^{2}} + {(3^{2})}^{\frac{1}{2}} - {(3^{2})}^{- \frac{1}{2}} = 1 + \frac{1}{9} - \frac{1}{81} + 3^{2 \times \frac{1}{2}} - 3^{2 \times (- \frac{1}{2})} = 1 + \frac{1}{9} - \frac{1}{81} + 3 - 3^{- 1} = 1 + \frac{1}{9} - \frac{1}{81} + \frac{3}{1} - \frac{1}{3} = \frac{81 + 9 - 1 + 243 - 27}{81} = \frac{333 - 28}{81} = \frac{305}{81} = 3 \frac{62}{81} \end{matrix}$

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Evaluate :

$(i) (- 5)^{\circ} (i i) 8^{\circ} + 4^{\circ} + 2^{\circ} (i i i) (8 + 4 + 2)^{\circ} (i v) 4 x^{\circ} (v) (4 x)^{\circ} (v i) [(10^{3})^{\circ}]^{5} (v i i) (7 x^{\circ})^{2} (v i i i) 9^{\circ} + 9^{- 1} - 9^{- 2} + 9^{\frac{1}{2}} - 9^{- \frac{1}{2}}$

Q. Evaluate:

(v i i i)

9^{0} + 9^{- 1} - 9^{- 2} + 9^{\frac{1}{2}} - 9^{\frac{- 1}{2}}

Q. Evaluate

\frac{1}{9} + \frac{2}{9}

Evaluate $3 \times {(9)}^{\frac{5}{2}} \times {(9)}^{\frac{- 1}{2}}$

Evaluate $\frac{- 9}{2} \div 1$

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Evaluate: 90+9−1−9−2+912−9−12

90+9−1−9−2+912−9−12=1+19−192+(32)12−(32)−12=1+19−181+32×12−32×(−12)=1+19−181+3−3−1=1+19−181+31−13=81+9−1+243−2781=333−2881=30581=36281

Evaluate:
$9^{0} + 9^{- 1} - 9^{- 2} + 9^{\frac{1}{2}} - 9^{- \frac{1}{2}}$