Problem 56 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(10 x^{2}\right)^{-3}$$

Step-by-Step Solution

Answer

The simplified form of the expression \((10x^2)^{-3}\) is \(1/(1000x^6)\).

Step 1: Identify the base and the exponent

The base is \(10x^2\) and the exponent is -3. This means the entire expression \((10x^2)\) is being raised to the power of -3.

Step 2: Apply the rule of negative exponents

The rule of negative exponents states that \(a^{-n} = 1/a^n\). This means that the expression \((10x^2)^{-3}\) can be rewritten as \(1/(10x^2)^3\).

Step 3: Simplify the expression

Now you have \(1/(10^3x^{2*3})\). To proceed, carry out the exponentiation: \(10^3=1000\) and \(2*3=6\). So, the expression simplifies to \(1/(1000x^6)\).