Question

Choose the correct simplification of (2xy7)2(y4)3.

Answer 1

2^2 = 4
answer starts with 4
(xy7)^2 = x^2 y(7*2) = x^2y^14
(y^4)^3 = y^(4*3) = y^12

answer is 4x^2 y^14*y^12
= 4x^2 y^(12+14)
= 4x^2y^26

D

Answer 2

The given expression
`\left(2xy^7\right)^2\left(y^4\right)^3` is simplified to
`4x^2y^(26)`

Explanation:

Given : Expression
`\left(2xy^7\right)^2\left(y^4\right)^3`

We have to write the correct simplification for the given expression
`\left(2xy^7\right)^2\left(y^4\right)^3`

Consider the given expression
`\left(2xy^7\right)^2\left(y^4\right)^3`

Apply exponent rule,
`\left(a\cdot \:b\right)^n=a^nb^n`

We have,

`=2^2x^2\left(y^7\right)^2`

Simplify, we have,

`=2^2x^2y^(14)`

Apply exponent rule,
`\left(a^b\right)^c=a^(bc)`

Simplify, we have,

`=y^(4\cdot \:3)=y^(12)`

Thus, The expression becomes,
`=2^2x^2y^(14)y^(12)`

Apply exponent rule,
`\:a^b\cdot \:a^c=a^(b+c)`

`y^(14)y^(12)=\:y^(14+12)=\:y^(26)`

Simplify, we have,

`=4x^2y^(26)`

Thus, The given expression
`\left(2xy^7\right)^2\left(y^4\right)^3` is simplified to
`4x^2y^(26)`