Question

What expression is equivalent to (it’s in the attached)

Answer 1

The answer to your question is the first option.

2x²y³
`\sqrt[3]{2x^(2)y}`

Explanation:

`\sqrt[3]{32x^(8)y^(10)  }`

Process

1.- Find the prime factors of 32

32 2

16 2

8 2

4 2

1

32 = 2 x 2 x 2 x2 = 2⁴

2.- Express as fractional exponents

=
`\sqrt[3]{2^(4) x^(8) y^(10) }`

=
`2^(4/3) x^(8/3) y^(10/3)`

3.- Simplify using exponent rules

=
`2^(3/3) 2^(1/3) x^(6/3) x^(2/3) y^(9/3) y^(1/3)`

= 2x²y³
`\sqrt[3]{2x^(2)y}`