simplify (x^2*y^2/a^2*b^3)^n
Answers
Answer:ANSWER:
(i)
3(a4b3)10×5(a2b2)3=3×a40×b30×5×a6×b6=15×a40×a6×b30×b6=15×a40+6×b30+6 [am×an=am+n]=15a46b36
(ii)
(2x-2y3)3=23×(x-2)3×(y3)3=8×x-6×y9=8x-6y9
(iii)
(4×107)(6×10-5)
8×104
=
4×107×6×10-5
8×104
=
24×107+(-5)
8×104
=
24×102
8×104
=
24×102×10-4
8
=3×102+(-4)=3×10-2=
3
100
(iv)
4ab2(-5ab3)
10a2b2
=
4×a×b2×(-5)×a×b3
10a2b2
=
-20×a1×a1×b2×b3
10a2b2
=
-20×a1+1×b2+3
10a2b2
=-2×a2×b5×a-2×b-2=-2×a2+(-2)×b5+(-2)=-2×a0×b3=-2b3
(v)
(
x2y2
a2b3
)n=
(x2)n(y2)n
(a2)n(b3)n
=
x2ny2n
a2nb3n
(vi)
(a3n-9)6
a2n-4
=
a6(3n-9)
a2n-4
=
a(18n-54)
a2n-4
=a(18n-54)×a-(2n-4)=a18n-54×a-2n+4=a18n-54-2n+4=a16n-50
Step-by-step explanation:ANSWER:
(i)
3(a4b3)10×5(a2b2)3=3×a40×b30×5×a6×b6=15×a40×a6×b30×b6=15×a40+6×b30+6 [am×an=am+n]=15a46b36
(ii)
(2x-2y3)3=23×(x-2)3×(y3)3=8×x-6×y9=8x-6y9
(iii)
(4×107)(6×10-5)
8×104
=
4×107×6×10-5
8×104
=
24×107+(-5)
8×104
=
24×102
8×104
=
24×102×10-4
8
=3×102+(-4)=3×10-2=
3
100
(iv)
4ab2(-5ab3)
10a2b2
=
4×a×b2×(-5)×a×b3
10a2b2
=
-20×a1×a1×b2×b3
10a2b2
=
-20×a1+1×b2+3
10a2b2
=-2×a2×b5×a-2×b-2=-2×a2+(-2)×b5+(-2)=-2×a0×b3=-2b3
(v)
(
x2y2
a2b3
)n=
(x2)n(y2)n
(a2)n(b3)n
=
x2ny2n
a2nb3n
(vi)
(a3n-9)6
a2n-4
=
a6(3n-9)
a2n-4
=
a(18n-54)
a2n-4
=a(18n-54)×a-(2n-4)=a18n-54×a-2n+4=a18n-54-2n+4=a16n-50