verify (a^2bc^2)(9ab^2c^2)(-4ab^2c^4)when a=1/2 and b=-1
Answers
Answer:
The product of the given expression is (a^2bc^2)(9ab^2c^2)(-4ab^2c^4)=-36a^4b^5c^8(a
2
bc
2
)(9ab
2
c
2
)(−4ab
2
c
4
)=−36a
4
b
5
c
8
Therefore the result for the given product when a=\frac{1}{2}a=
2
1
,b=-1 and c=1 is \frac{3}{2}
2
3
Step-by-step explanation:
Given expression is (a^2bc^2)(9ab^2c^2)(-4ab^2c^4)(a
2
bc
2
)(9ab
2
c
2
)(−4ab
2
c
4
)
To find the product of the given expression :
(a^2bc^2)(9ab^2c^2)(-4ab^2c^4)(a
2
bc
2
)(9ab
2
c
2
)(−4ab
2
c
4
)
Combining the like terms
=((9)(-4))((a^2)(a)(a))((b)(b^2)(b^2))((c^2)(c^2)(c^4))=((9)(−4))((a
2
)(a)(a))((b)(b
2
)(b
2
))((c
2
)(c
2
)(c
4
))
=(-36)(a^{2+1+1})(b^{1+2+2})(c^{2+2+4})=(−36)(a
2+1+1
)(b
1+2+2
)(c
2+2+4
)
=-36a^4b^5c^8=−36a
4
b
5
c
8
Therefore the product of the given expression is (a^2bc^2)(9ab^2c^2)(-4ab^2c^4)=-36a^4b^5c^8(a
2
bc
2
)(9ab
2
c
2
)(−4ab
2
c
4
)=−36a
4
b
5
c
8
Now to verify the result for a=\frac{1}{2}a=
2
1
,b=-1 and c=1 :
The result is -36a^4b^5c^8−36a
4
b
5
c
8
Put the values of a=\frac{1}{2}a=
2
1
,b=-1 and c=1 in the above result
=-36(\frac{1}{2})^4(-1)^5(1)^8=−36(
2
1
)
4
(−1)
5
(1)
8
=-36(\frac{1}{16})(-1)(1)=−36(
16
1
)(−1)(1)
=\frac{3}{2}=
2
3
Therefore the result for the given product when a=\frac{1}{2}a=
2
1
,b=-1 and c=1 is \frac{3}{2}
2
3
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