Question

What is the following simplified product? Assume x greater-than-or-equal-to 0 (StartRoot 6 x squared EndRoot 4 StartRoot 8 x cubed EndRoot) (StartRoot 9 x EndRoot minus x StartRoot 5 x Superscript 5 Baseline) 3 x StartRoot 6 x EndRoot x Superscript 4 Baseline StartRoot 30 x EndRoot 24 x squared 8 x Superscript 5 Baseline StartRoot 10 x EndRoot 3 x StartRoot 6 x EndRoot x Superscript 4 Baseline StartRoot 30 x EndRoot 24 x squared StartRoot 2 EndRoot 8 x Superscript 5 Baseline StartRoot 10 EndRoot 3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot 24 x squared StartRoot 2 EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 EndRoot 3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot 24 x squared StartRoot 2 x EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 x EndRoot.

Answer 1

The question is about simplifying a mathematical expression involving various powers and roots of 'x'. We utilize exponent rules like product of powers and power of a power in the simplification process.

Step-by-step explanation:

The student has asked for help with simplifying a complex mathematical expression assuming x ≥ 0. Simplification of such expressions often involves using exponent rules including the product of powers, power of a power, and properties of square roots.

One of the important rules we use is that x² is equivalent to √x (square root of x), because when you multiply the square root of a number by itself, you end up with the original number. For example: (5³)⁴ = 5¹²; you multiply the exponents (3 and 4) here to get 12.

When you multiply two quantities with the same base, you can simply add the exponents. Conversely, when dividing, you subtract the exponents. Also, any number raised to the zero power equals 1. For example: 3⁴ × 3⁻⁴ = 3° = 1.