Question

Which expression is equivalent to (256x^16)^1/4? 4x2 4x4 64x2 64x4

Answer 1

`(256x^(16))^(1)/(4)=(2^8x^(16))^(1)/(4)\\\\Use:\ (ab)^n=a^nb^n\ and\ (a^n)^m=a^(nm)\\\\=(2^8)^(1)/(4)(x^(16))^(1)/(4)=2^{8\cdot(1)/(4)}x^{16\cdot(1)/(4)}=2^2x^4=4x^4\\\\Answer:\ \boxed{(256x^(16))^(1)/(4)=4x^4}`

Answer 2

`=[256x^(16)]^(1)/(4)\\\\=[(4 * 4 * 4* 4* x^(16)]^(1)/(4)\\\\ =[(4^4)^{(1)/(4)}* [x^(16)]{(1)/(4)}\\\\ =4 * x^4\\\\={\text{Using the property}} (ab)^(1)/(m)=a^(1)/(m) b^(1)/(m)\\\\{\text{also}} (a^m){(1)/(n)}=a^{(m)/(n)}`

Factorizing 256,and,
`x^(16)`

256= 2×2×2×2×2×2×2×2=4×4×4

`x^(16)=x^4* x^4* x^4* x^4`

Option (B)
`4 x^4` is true.