Answer :
Answer:
k = 4
Step-by-step explanation:
Given: [tex](5a^2b^3)(6a^kb)=30a^6b^4[/tex]
Exponent law:
[tex]x^m\cdot x^n=x^{m+n}[/tex]
[tex]x^m\div x^n=x^{m-n}[/tex]
[tex]5\cdot 6\cdot a^2\cdot a^k\cdot b^3\cdot b=30a^6b^4[/tex]
[tex]30a^{2+k}b^{3+1}=30a^6b^4[/tex]
Compare the coefficient and power both sides
[tex]30=30[/tex]
[tex]a^{2+k}=a^6[/tex]
[tex]b^4=b^4[/tex]
Exponent must be equal if base is equal.
Thus, 2+k = 6
k = 6 - 2
k = 4
Hence, The vaue of k is 4