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

Multiplication and Division with Exponents

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Fractions and decimals for KS4
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Indices with rational exponents
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:multiplication_and_division_with_exponents/3597/


Example 1.

Calculate

   
Example 2.

Calculate and leave the result as a fraction.

    
3.

Calculate and leave the result in a form of fraction.

    
4.

Calculate as a fraction.

    
5.

Calculate

   
6.

Rationalize:


    
7.

Evalulate the following:








    
8.
Simplify:

    

9.
Calculate:

    
10.
Calculate:

    
11.
Write down the powers with rational exponents and calculate.

    
12.

Simplify the expression:


    
13.
Calculate:

    
14.
Calculate:

    
15.
Calculate:

    
16.
Calculate:

    
17.

Calculate .

    
18.
Calculate:

    

19.
Calculate:

    
20.
Calculate:

    
21.
Calculate:

    
22.
Write with the roots first and then calculate exactly.

    
23.
Using a pocket calculator, calculate the next root and round the result to three places exactly.

    
24.
Check to see if it applies.

    
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.

Simplify the expression .