Final answer:
To solve the equation, we apply the rules of exponents, including cubing of exponentials and division of exponentials. After simplifying the equation, we find that x equals 1.
Step-by-step explanation:
To find the value of x that makes the equation ((b¹⁰)³) / b¹⁵ = b¹⁸ * bˣ / b⁸ true, we apply the rules of exponents for multiplication and division. First, we'll address the exponentiation of an exponent. According to the cubing of exponentials, when cubing b to the tenth power, we multiply the exponents: (b¹⁰)³ = b⁰. Similarly, for multiplication of exponentials: b¹⁸ * bˣ = b¹⁸⁴
Next, for division of exponentials, you subtract the exponent in the denominator from the exponent in the numerator. Our original equation simplifies to b³⁰ / b¹⁵ = b¹⁸⁴ / b⁸. Subtracting the exponents gives us: b±⁵ = b¹⁰⁴⁴⁽
Finally, to solve for x, we equate the exponents on both sides. We know that b±⁵ must equal b¹⁰⁴⁴⁽, therefore x must be equal to 15 - (18 + 4 - 8), which simplifies to 15 - 14 = 1. Therefore, x = 1.