Question

Which expression is equivalent to (4y^2)^3 (3y^2)

Answer 1

192y^8 is your answer

Answer 2

Given expression:
`\left(4y^2\right)^3\left(3y^2\right)`.

`\mathrm{Apply\:exponent\:rule}:\quad \left(ab\right)^c=a^cb^c`

`\left(4y^2\right)^3=4^3\left(y^2\right)^3`

`\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^(bc)`

`\left(y^2\right)^3=y^(2\cdot \:3)=y^6`

`\left(4y^2\right)^3\cdot \:3y^2=4^3y^6\cdot \:3y^2`

`\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)`

`y^6y^2=\:y^(6+2)=\:y^8`

`=4^3\cdot \:3y^8`

`=192y^8`

Therefore,
`192y^8` expression is equivalent to
`\left(4y^2\right)^3\:\left(3y^2\right)`.