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Simplify: ( 4 − 1 × 3 − 1 ) 2 - Mathematics

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प्रश्न

Simplify:

\[\left( 4^{- 1} \times 3^{- 1} \right)^2\]
योग

उत्तर

`(4^(-1)xx3^(-1))^2-(1/4xx1/3)^2`     `->(a^(-1)=1/a)`

`=(1/12)^2`

`=1^2/12^2`    `->(a/b)^n=(a^n)/(b^n)`

`=1/24`

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अध्याय 2: Powers - Exercise 2.1 [पृष्ठ ८]

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आरडी शर्मा Mathematics [English] Class 8
अध्याय 2 Powers
Exercise 2.1 | Q 4.1 | पृष्ठ ८

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संबंधित प्रश्न

Simplify and express the result in power notation with positive exponent.

`(1/2^3)^2`


Express the following as a rational number of the form \[\frac{p}{q},\] where p and q are integers and q ≠ 0.

\[\frac{1}{3^{- 2}}\]

 


Write the following in exponential form:

\[\left( \frac{3}{2} \right)^{- 1} \times \left( \frac{3}{2} \right)^{- 1} \times \left( \frac{3}{2} \right)^{- 1} \times \left( \frac{3}{2} \right)^{- 1}\]

Express the following rational numbers with a positive exponent:

\[4^3 \times 4^{- 9}\]

Simplify:

\[\left\{ \left( \frac{2}{3} \right)^2 \right\}^3 \times \left( \frac{1}{3} \right)^{- 4} \times 3^{- 1} \times 6^{- 1}\]

Which of the following is not equal to \[\left( \frac{- 3}{5} \right)^4 ?\]


\[\left( \frac{- 1}{2} \right)^5 \times \left( \frac{- 1}{2} \right)^3\] is equal to

\[\left( \frac{1}{5} \right)^0\]  is equal to

For a non-zero rational number a, a7 ÷ a12 is equal to


Predicting the ones digit, copy and complete this table and answer the questions that follow.

 Powers Table
x 1x 2x 3x 4x 5x 6x 7x 8x 9x 10x
1 1 2                
2 1 4                
3 1 8                
4 1 16                
5 1 32                
6 1 64                
7 1 128                
8 1 256                
Ones
Digits
of the
Powers
1 2, 4, 8, 6                
  1. Describe patterns you see in the ones digits of the powers.
  2. Predict the ones digit in the following:
    1. 412
    2. 920
    3. 317
    4. 5100
    5. 10500
  3. Predict the ones digit in the following:
    1. 3110
    2. 1210
    3. 1721
    4. 2910 

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