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mathematics UK Year 10 Mathematics (KS4)
 
Solved problems for the chapter:
 

Indices I

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Indices with integer exponents
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Exponential equation and inequality
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Fractions and decimals for KS4
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Indices with rational exponents
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Indices with natural exponents for KS4
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↓   Show theory [5]   ↓


Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:indices_i/5301/


Example 1.

Simplify:


    
Example 2.
Simplify the expression:

    
3.
Simplify the expression:

    
4.

Calculate:


    
5.

Solve for the value of in the equation

   
6.

Solve the exponential equation

   
7.

Solve for in the equation

   
8.

Calculate

   

9.

Calculate and leave the result as a fraction.

    
10.

Calculate and leave the result in a form of fraction.

    
11.

Calculate as a fraction.

    
12.

Calculate

   
13.
Calculate:

    
14.
Calculate:

    
15.
Write down the powers with rational exponents and calculate.

    
16.
Calculate:

    
17.
Calculate:

    
18.
Calculate:

    

19.

Calculate .

    
20.
Calculate:

    
21.
Calculate:

    
22.

Calculate:


    
23.
Write with the roots first and then calculate exactly.

    
24.
Using a pocket calculator, calculate the next root and round the result to three places exactly.

    
25.
Write down the powers with rational exponents and calculate.

    
26.
Using a pocket calculator, calculate the next root and round the result to three places exactly.

    
27.
Using a pocket calculator, calculate the next root and round the result to three places exactly.

    
28.

For which integers and apply:


    

29.

Evaluate the following:


.

    
30.

Evaluate:


    
31.

Evaluate:


    
32.

Express in index form:


16, 27, 81, 121, 125

    
33.

Evaluate:


    
34.

Express the following numbers in index form: 10, 100, 1000, 10000, 100000.

    
35.

Evaluate:


    
36.

Simplify

   
37.

Calculate:


    
38.

Evaluate:

   

39.

Arrange in ascending order.

    
40.

Arrange in ascending order.

    
41.

Evaluate:

   
42.

Evaluate:

   
43.

Evaluate:

   
44.

Calculate exactly:


    
45.

evaluate:

   
46.

Verify if the equality is valid:

   
47.

Evaluate:

   
48.

Calculate:

   

49.

Calculate:

   
50.

Evaluate:

   
51.

Evaluate:

   
52.

Calculate:


    
53.

Calculate:

   
54.

Calculate:


    
55.

Factorise:

   
56.

Calculate:


    
57.

Evaluate:

   
58.

Calculate:


    

59.

Simplify:


    
60.

Calculate the value of the expression: