Find the value of 'a' if `[(-3)^3]^(5) =(-3)^(3a)`.

Answer

To solve the equation \([(-3)^3]^{5} = (-3)^{3a}\), we will follow these steps:

### Step 1: Simplify the left-hand side
Using the property of exponents that states \((a^m)^n = a^{m \cdot n}\), we can simplify the left-hand side:

\[ [(-3)^3]^{5} = (-3)^{3 \cdot 5} = (-3)^{15} \]

### Step 2: Rewrite the equation
Now, we can rewrite the equation with the simplified left-hand side:

\[ (-3)^{15} = (-3)^{3a} \]

### Step 3: Equate the exponents
Since the bases are the same (both are \(-3\)), we can equate the exponents:

\[ 15 = 3a \]

### Step 4: Solve for 'a'
To find the value of \(a\), divide both sides of the equation by 3:

\[ a = \frac{15}{3} = 5 \]

### Final Answer
Thus, the value of \(a\) is \(5\).

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