Respuesta :

calculista

we have

[tex]2ab(\sqrt[3]{192ab^{2}}) -5(\sqrt[3]{81a^{4}b^{5}})[/tex]

we know that

[tex]192=3*4^{3} \\81= 3^{4}[/tex]

Substitute in the expression above

[tex]=2ab(\sqrt[3]{3*4^{3}ab^{2}}) -5(\sqrt[3]{3^{4}a^{4}b^{5}})[/tex]

remember that

[tex]\sqrt[3]{4^{3}}=4\\ \\ \sqrt[3]{3^{4}a^{4}b^{5}}=3ab \sqrt[3]{3ab^{2}}[/tex]

Substitute

[tex]=2ab(4)(\sqrt[3]{3ab^{2}}) -5(3)(a)(b)(\sqrt[3]{3ab^{2}})[/tex]

[tex]=8ab(\sqrt[3]{3ab^{2}}) -15ab(\sqrt[3]{3ab^{2}})[/tex]

[tex]=-7ab(\sqrt[3]{3ab^{2}})[/tex]

therefore

the answer is

[tex]-7ab(\sqrt[3]{3ab^{2}})[/tex]

MrRoyal

Equivalent expressions are expressions with equal values

The difference of [tex]2ab[\sqrt[3]{192ab^2}] - 5[\sqrt[3]{81a^4b^5}][/tex] is [tex]-7ab\sqrt[3]{3ab^2}[/tex]

The expression is given as:

[tex]2ab[\sqrt[3]{192ab^2}] - 5[\sqrt[3]{81a^4b^5}][/tex]

Rewrite the above expression as:

[tex]2ab[\sqrt[3]{3 * 4^3 * ab^2} ]- 5[\sqrt[3]{3 * 3^3 * a^4b^5}][/tex]

Evaluate the cube roots

[tex]2ab[4\sqrt[3]{3 ab^2} ]- 5[3ab\sqrt[3]{3ab^2}][/tex]

Evaluate the products

[tex]8ab\sqrt[3]{3 ab^2}- 15ab\sqrt[3]{3ab^2}[/tex]

Evaluate the differences

[tex]-7ab\sqrt[3]{3ab^2}[/tex]

Hence, the difference of [tex]2ab[\sqrt[3]{192ab^2}] - 5[\sqrt[3]{81a^4b^5}][/tex] is [tex]-7ab\sqrt[3]{3ab^2}[/tex]

Read more about equivalent expressions at:

https://brainly.com/question/2972832

Otras preguntas