Question

Simplify the following Questions. (IMPORTANT NOTE!!! #'s 2 AND 7 MUST BE IN SCIENTIFIC NOTATION!!!!!) 1.) (x)²(2xy³)^5 2.) (4x10^8)^2 3.) (-h^4)^5 4.) (3xy³)²(xy)^6 5.) (p^9)^-2 6.)(5k²)³ 7.)(7x10^5)² 8.)(x)³(-x³y)² 9.)w^5(w²)^-4 10.) (2x^5)^4

Answer 1

Explanation:

Hint :

`(a*b)^(m)= a^(m)b^(m)\\\\\\(a^(m))^(n)=a^(mn)\\\\\\a^(m)*a^(n)=a^(m+n)\\`

`1)x^(2)(2xy^(3))^(5)=x^(2)*2^(5)*x^(5)*(y^(3))^(5)\\\\\\=x^(2)*2^(5)*x^(5)*y^(3*5)\\\\=x^(2)*2^(5)*x^(5)*y^(15)\\\\=2^(5)*x^(2+5)*y^(15)\\\\=2^(5)x^(7)y^(15)`

`2) (4x10^(8))^(2)=4^(2)*x^(2)*(10^(8))^(2)\\\\=16*x^(2)*10^(8*2)\\\\=1.6*10*x^(2)*10^(16)\\\\=1.6x^(2)*10^(16+1)\\\\=1.6x^(2)10^(17)`

`3)(-h^(4))^(5)=(-h)^(4*5)=-h^(20)\\\\\4)(3xy^(3))^(2)(xy)^(6)=3^(2)x^(2)(y^(3))^(2)x^(6)y^(6)\\\\=9x^(2)y^(3*2)x^(6)y^(6)\\\\\\=9x^(2)y^(6)x^(6)y^(6)\\\\=9x^(2+6)y^(6+6)\\\\=9x^(8)y{12}\\\\\\`

`5) (p^(9))^(-2)=p^(9*-2)=p^(-18)\\\\\\6)(5k^(2))^(3)=5^(3)(k^(2))^(3)=625k^(6)\\\\7)(7x10^(5))^(2)=7^(2)x^(2)(10^(5))^(2)\\\\=49x^(2)10^(5*2)\\\\=4.9*10^(1)x^(2)10^(10)\\\\=4.9x^(2)10^(10+1)\\\\=4.9x^(2)10^(11)`

`8)x^(3)(-x^(3)y)^(2)=x^(3)*(-x^3})^(2)y^(2)\\\\\\=x^(3)*(-1)^(2)*x^(2*3)y^(2)\\\\=x^(3)*1*x^(6)y^(2)=x^(3+6)y^(2)\\\\=x^(9)y^(2)\\\\\\9)w^(5)(w^(2))^(-4)=w^(5)w^(2*-4)\\\\=w^(5)w^(-8)\\\\=w^(5-8)=w^(-3)\\\\=(1)/(w^(3))\\\\\\10) (2x^(5))^(4)=2^(4)x^(5*4)\\\\=2^(4)x^(20)\\\\=16x^(20)`