Question

Simplify the expression 3x3^ 648x 4 y8

Answer 1

Answer:

B. $18x^{2} y^{2} \sqrt[3]{3xy^{2} }$

Step-by-step explanation:

To simplify this expression, use the fact that the root of a number (in this case is the cube root)  can be expressed like a fractional exponent (1/3). Using this, the expression changes to:

$3x(648x^{4}y^{8})^{(1/3)}$

Next step is to put the exponent inside the parenthesis:

$3x(648^{1/3}x^{4/3}y^{8/3})$

Find the prime factorization  of 648:

648 =3⋅3⋅3⋅3⋅2⋅2⋅2

648=3⁴∗2³

$3x(3^{(4/3)}2^{(3/3)}x^{4/3}y^{8/3})$

Change all improper fractions in exponent to mixed fractions

$3x(3^{1(1/3)}2^{1}x^{1(1/3)}y^{2(2/3)})$

Separate integers exponents from fractional:

$3x(3\cdot3^{(1/3)}\cdot 2 \cdot x\cdot x^{1/3}\cdot y^{2}\cdot y^{2/3})$

Re-arrange (all numbers with fractional exponents must be together):

$3x(3 \cdot 2\cdot x\cdot y^{2}\cdot 3^{(1/3)}x^{1/3}y^{2/3})$

Multiply the 3x with the numbers that have an integer exponent:

$18x^{2}y^{2}(3^{(1/3)}x^{1/3}y^{2/3})$

Take out  the exponent 1/3 from the parenthesis:

$18x^{2}y^{2}(3xy^{2})^{1/3}$

And change the representation of the root to use a radical symbol

$18x^{2} y^{2} \sqrt[3]{3xy^{2} }$

Answer 2

Answer: B.)      18x^2y^2 3squareroot 3xy^2

Step-by-step explanation: