Radicals and Exponents Evaluate each expression: a) 2 sqrt[3]{81} b) frac{sqrt{18}}{sqrt{25}} c) sqrt{frac{12}{49}}

Aneeka Hunt

Aneeka Hunt

Answered question

2020-12-25

Radicals and Exponents Evaluate each expression: 
a) 2813 
b) 1825 
c) 1249

Answer & Explanation

mhalmantus

mhalmantus

Skilled2020-12-26Added 105 answers

a) Formula for nth root: 
an=a1n 
Laws of exponents: 
(am)n=amn 
Calculation: 
Use the above-mentioned formula and simplify the expression 2813 as shown below. 
2813=2343 
=2  (34)13 
=2  343 
=2  313  333 
On further simplification of the above equation, the following is obtained. 
2813=2  3  313 
=633 
Therefore, the value of expression 2813 is 633. 
b) Use the formula mentioned in part (a) and simplify the expression 1825 as shown below. 
1825=9  25  5 
=(32)12  2(52)12 
=325 
Therefore, the value of expression 1825 is 325 
c) Use the formula mentioned in part (a) and simplify the expression as shown below. 
1249=4  37  7 
=(22)12 3(72)12 
=237 
Therefore, the value of expression 1249 is 237.

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