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

Aneeka Hunt 2020-12-25 Answered
Radicals and Exponents Evaluate each expression:
a) 23{81}
b) 1825
c) 1249
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Expert Answer

mhalmantus
Answered 2020-12-26 Author has 106 answers
a) Formula for nth root:
n{a}=a1n
Laws of exponents:
(am)n=amn
Calculation:
Use the above-mentioned formula and simplify the expression 23{81} as shown below.
23{81}=23{34}
=2  (34)13
=2  343
=2  313  333
On further simplification of the above equation, the following is obtained.
23{81}=2  3  313
=63{3}
Therefore, the value of expression 23{81} is 63{3}.
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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