## Simplifying the Expression: (a^3)^-1/3 x (a^2)^1/2

This article aims to simplify the given mathematical expression: **(a^3)^-1/3 x (a^2)^1/2**.

To understand how to simplify this expression, we need to recall some key exponent rules:

**(a^m)^n = a^(m*n)**: When raising a power to another power, we multiply the exponents.**a^m * a^n = a^(m+n)**: When multiplying powers with the same base, we add the exponents.**a^-n = 1/a^n**: A negative exponent indicates the reciprocal of the base raised to the positive power.

Let's break down the simplification step by step:

### Step 1: Apply the first rule to both terms.

**(a^3)^-1/3 = a^(3 * -1/3) = a^-1****(a^2)^1/2 = a^(2 * 1/2) = a^1 = a**

### Step 2: Substitute the simplified terms into the original expression.

Our expression now becomes: **a^-1 * a**

### Step 3: Apply the second rule to simplify further.

**a^-1 * a = a^(-1 + 1) = a^0**

### Step 4: Apply the third rule to simplify the final result.

**a^0 = 1**

Therefore, the simplified form of the expression **(a^3)^-1/3 x (a^2)^1/2** is **1**.