Solution:
Law of indices
[tex]1.a ^m \times a ^n= a^{m+n} 2. \frac{a^m}{a^n}=a^{m-n} 3. a^m \times b^m=(ab)^{m}[/tex]
1.
[tex]\frac{1}{2}\times a^4\times b^2\\\\ =\frac{1}{2}\times(-2)^4\times(4)^2\\\\ =\frac{1}{2}\times2^4\times (2^2)^2\\\\ =2^{4+4-1}\\\\ 2^7=128[/tex]
2.
A number raised to a negative exponent is negative.=False Statement
because, [tex]a^{-m}=\frac{1}{a^m}[/tex]
=Option (C) sometimes because [tex](-3)^{-3}=\frac{-1}{27}[/tex]
3.
[tex](4xy^2)^3(xy)^5 =4^3\times x^3 \times x^5\times y^6 \times y^5\\\\ =64 x^8 y^{11}[/tex]
=Option (A)
4.
[tex]= (2t^3)^3(0.4r)^2\\\\= 2^3\times (t^3)^3*(0.4)^2*r^2\\\\= 8 *0.16 *t^9*r^2\\\\=1.28 t^9 r^2[/tex]
