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प्रश्न
Find the value of the following:
(30 + 4−1) × 22
बेरीज
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उत्तर
We know from the property of powers that for every natural number a, a−1 = 1/a.
Moreover, a0 is 1 for every natural number a not equal to 0. Then:
\[\left( 3^0 + 4^{- 1} \right) \times 2^2 \]
\[ = \left( 1 + \frac{1}{4} \right) \times 4 \left[ as, a^{- 1} = \frac{1}{a}; a^0 = 1 \right]\]
\[ = \frac{5}{4} \times 4\]
\[ = 5\]
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संबंधित प्रश्न
Evaluate.
(−4)−2
Find the value of the following:
(2−1 × 4−1) ÷ 2−2
Simplify:
\[\left( 3^2 - 2^2 \right) \times \left( \frac{2}{3} \right)^{- 3}\]
Simplify:
\[\left\{ 3^{- 1} \times 4^{- 1} \right\}^{- 1} \times 5^{- 1}\]
Express the following rational numbers with a negative exponent:
\[\left\{ \left( \frac{3}{2} \right)^4 \right\}^{- 3}\]
Express the following rational numbers with a positive exponent:
\[\left\{ \left( \frac{4}{3} \right)^{- 3} \right\}^{- 4}\]
Simplify:
\[\left\{ \left( \frac{1}{2} \right)^{- 1} \times ( - 4 )^{- 1} \right\}^{- 1}\]
Find x, if
\[\left( \frac{3}{2} \right)^{- 3} \times \left( \frac{3}{2} \right)^5 = \left( \frac{3}{2} \right)^{2x + 1}\]
if \[x = \left( \frac{3}{2} \right)^2 \times \left( \frac{2}{3} \right)^{- 4}\], find the value of x−2.
\[\left\{ \left( \frac{1}{3} \right)^2 \right\}^4\] is equal to
