## Solving for the Unknown Exponent

The equation (5a²b³)(6a^kb) = 30a⁶b⁴ presents a challenge: finding the value of *k* that makes the equation true. Let's break down the steps to solve this:

### 1. Simplify the Left Side

**Multiply the coefficients:**5 * 6 = 30**Combine the 'a' terms:**a² * a^k = a^(2+k)**Combine the 'b' terms:**b³ * b = b^(3+1) = b⁴

Now, the simplified left side of the equation is **30a^(2+k)b⁴**

### 2. Compare Coefficients and Exponents

The equation now reads: **30a^(2+k)b⁴ = 30a⁶b⁴**

To make the equation true, both sides must have the same coefficients and exponents for each variable.

**Coefficients:**We already see that the coefficients (30) match on both sides.**Exponents:**We need to ensure that the exponents for 'a' and 'b' match on both sides.

### 3. Solve for 'k'

**'a' exponent:**2 + k = 6**Solve for 'k':**k = 6 - 2 = 4

### Conclusion

Therefore, the value of *k* that satisfies the equation (5a²b³)(6a^kb) = 30a⁶b⁴ is **k = 4**.