%5E-1%2F3-x-(a%5E2)%5E1%2F2.jpeg "(a^3)^-1/3 X (a^2)^1/2")
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.