To simplify: The expression and eliminate coefficients if any: a) sqrt[4]{b^{3}} sqrt{b} b) (2sqrt{a}) (sqrt[3]{a^{2}})

slaggingV 2021-02-01 Answered
To simplify: The expression and eliminate coefficients if any:
a) 4{b3} b
b) (2a) (3{a2})
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Expert Answer

gwibdaithq
Answered 2021-02-02 Author has 84 answers
a) Definition used:
Definition of rational exponents:
"For any rational exponent mn in its lowest terms, where m and n are integers and n > 0 we define, (a)mn=n{(a)m}=(n{a})m
Formula used:
"The product of two powers with the same base a and different exponents m and n is given by, am × an=am + n
That is, while multiplying two powers with same base, the exponents are added and the base will remain the same.
Calculation:
The given expression is 4{b3} b.
Use the definition of rational exponents and the above formula and simplify the expression as shown below.
4{b3} b=b34  b12
=b34 +12
=b54
Therefore, the simplified form of the expression is b54
b) Use the definition of rational exponents and the formula mentioned in sub part (a) and simplify the expression as shown below.
(2a) (3{a2})=(2a12) (a23)
=2a12 + 23
=2a76
Therefore, the simplified form of the expression is 2a76
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