what value of k makes the equation true?\n$(5a^{2}b^{3})(6a^{k}b)=30a^{6}b^{4}$\n2\n3\n4\n8
what value of k makes the equation true?\n$(5a^{2}b^{3})(6a^{k}b)=30a^{6}b^{4}$\n2\n3\n4\n8
Answer
Explanation:
Step1: Multiply the coefficients and use exponent rule
Multiply (5) and (6) (coefficients). For the variables, use the rule (a^m\times a^n=a^{m + n}). So ((5a^{2}b^{3})(6a^{k}b)=(5\times6)a^{2 + k}b^{3+1}=30a^{2 + k}b^{4})
Step2: Equate the exponents of (a)
Since (30a^{2 + k}b^{4}=30a^{6}b^{4}), then (2 + k=6)
Step3: Solve for (k)
Subtract (2) from both sides of the equation (2 + k=6). We get (k=6 - 2)
Answer:
(k = 4) (the third option)