Jasonbradley
Home

(a^3)^-1/3 X (a^2)^1/2

2 min read Jun 16, 2024
(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.

Related Post

Featured Posts