contestada

What value of k makes the equation true?
(5a²b³)(6a^k(b))=30a^6(b^4)

A)2
B)3
C)4
D)8

Respuesta :

leeandrews2
when you multiply exponents, Your add them so you need to add 4 and 2 to get 6. The answer would be C
calculista

we have

[tex](5a^{2} b^{3} )(6a^{k}b)=30 a^{6}b^{4}[/tex]

Multiply the left side and then compare with the right side

[tex](5a^{2} b^{3} )(6a^{k}b)[/tex]

Combine like terms

[tex](5*6)(a^{2}*a^{k})(b^{3}*b)\\=(30)(a^{k+2})(b^{4})[/tex]

Compare with the right side

[tex](30)(a^{k+2})(b^{4})=30 a^{6}b^{4}[/tex]

so

[tex](a^{k+2})=a^{6}[/tex]

[tex]k+2=6[/tex]

solve for k

[tex]k=6-2=4[/tex]

therefore

the answer is the option C

[tex]4[/tex]

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