Question

Simplify the given expression. Assume x doesn’t = 0. (20x⁻³/10x⁻¹)⁻²

a. X⁴/²
b. X⁴/⁴
c. X²/⁴

Answer 1

The given expression (20x^{-3}/10x^{-1})^{-2} simplifies to x^4/4 using the rules of division of exponentials and properties of exponents.

Step-by-step explanation:

The student has been asked to simplify the expression (20x^{-3}/10x^{-1})^{-2}. To simplify this expression, we need to use the rules of division of exponentials and properties of exponents.

First, we simplify the base fractions and subtract the exponents:
(20/10) x^{-3 - (-1)} = 2x^{-3 + 1} = 2x^{-2}

Now we apply the negative exponent to the power of -2:

(2x^{-2})^{-2} = 2^{-2} x^{-2 * -2} = 1/4 x^4

Therefore, the simplified expression is x^4/4.