Question

mark true or false. if false, write the correct answer.

1. $2(16x^{2}yz^{4} - 13x^{2}yz^{4})^{3} = 18x^{6}y^{3}z^{12}$

true
false

1. $(-x^{5}y^{8}z)^{4} + (x^{20}y^{32}z^{4}) = 0$

true
false

1. $2(x^{9}y^{5})^{2} - (4x^{18}y^{10})^{\frac{1}{2}} = 2x^{18}y^{10}$

true
false

Explanation:

Step1: Simplify expression 1 inside parentheses

$16x^2yz^4 - 13x^2yz^4 = 3x^2yz^4$

Step2: Cube the simplified term

$(3x^2yz^4)^3 = 3^3 \cdot (x^2)^3 \cdot y^3 \cdot (z^4)^3 = 27x^6y^3z^{12}$

Step3: Multiply by the leading coefficient

$2 \cdot 27x^6y^3z^{12} = 54x^6y^3z^{12}$

Step4: Simplify expression 2 first term

$(-x^5y^8z)^4 = (-1)^4 \cdot (x^5)^4 \cdot (y^8)^4 \cdot z^4 = x^{20}y^{32}z^4$

Step5: Add the second term for expression 2

$x^{20}y^{32}z^4 + x^{20}y^{32}z^4 = 2x^{20}y^{32}z^4$

Step6: Simplify expression 3 first term

$2(x^9y^5)^2 = 2 \cdot (x^9)^2 \cdot (y^5)^2 = 2x^{18}y^{10}$

Step7: Simplify expression 3 second term

$(4x^{18}y^{10})^{\frac{1}{2}} = 4^{\frac{1}{2}} \cdot (x^{18})^{\frac{1}{2}} \cdot (y^{10})^{\frac{1}{2}} = 2x^9y^5$

Step8: Subtract terms for expression 3

$2x^{18}y^{10} - 2x^9y^5$

Answer:

1. False, correct answer: $54x^6y^3z^{12}$
2. False, correct answer: $2x^{20}y^{32}z^4$
3. False, correct answer: $2x^{18}y^{10} - 2x^9y^5$