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Applying properties of Exponents in exercise,use the properties of exponents to simplify the expression.See example 1.

(a) 5^3/25^2
(b) (92/3)(3)(32/3)
(c) [(251/2)(52)]1/3
(d) (82)(43)

User MandisaW
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1 Answer

3 votes

Answer: a)
(1)/(5) b) 27 c) 5 d)
2^(12)=4096

Explanation:

Properties of exponent :


  1. a^m* a^n= a^(m+n)

  2. (a^m)/(a^n)=a^(m-n)

  3. (a^m)^n=a^(mn)

  4. a^(-n)=(1)/(a^n)

By using above properties we simplify the given expressions.

a)
(5^3)/(25^2)=(5^3)/((5^2)^2)


=(5^3)/(5^4) [ By using (3)]


=5^(3-4)=5^(-1) [ By using (2)]


=(1)/(5) [ By using (4)]

b)
(9^{(2)/(3)})(3)(3^{(3)/(2)})


=((3^(2))^{(2)/(3)})(3^{1+(3)/(2)}) [ By using (1)]


=(3^{(4)/(3)})(3^{(5)/(2)}) [ By using (3)]


=3^{(4)/(3)+(5)/(3)} [ By using (1)]


=3^{(4+5)/(3)}=3^{(9)/(3)=3^3=27}

c)
[(25)^(1)/(2)(5^2)]^{(1)/(3)} =[(5^2)^(1)/(2)(5^2)]^(1)/(3)


=[(5)(5^2)]^(1)/(3) [ By using (3)]


=[5^(1+2)]^(1)/(3) [ By using (1)]


=5^{3*(1)/(3)})= 5 [ By using (3)]

d)
(8^2)(4^3)= (2^3)^2((2^2)^3) [ By using (5)]


=(2^6)(2^6) [ By using (3)]


=2^(6+6)=2^(12)=4096

User Orthehelper
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