When fully simplified, ignoring non-permissible values,24x^18/6x^3 x x^8/30x^6?
a)15/2x^8
b)2/15x^8
c)15/2x^17
d)2/15x^17
(24x^18/6x^3xX^8)/30x^6 = 4x^6/30x^6 =
2/15.
To simplify the expression (24x^18/6x^3) * (x^8/30x^6), you can follow these steps:
Step 1: Simplify within each fraction separately by combining the coefficients and exponents.
In the first fraction (24x^18/6x^3), divide the coefficients (24/6 = 4) and subtract the exponents (18-3 = 15). This gives us (4x^15).
Similarly, in the second fraction (x^8/30x^6), divide the coefficient (1/30 = 1/30) and subtract the exponents (8-6 = 2). This gives us (1/30x^2).
Step 2: Multiply the simplified fractions together.
Multiply (4x^15) * (1/30x^2) using the multiplication properties of exponents. Multiply the coefficients (4 * 1/30 = 4/30) and add the exponents (15 + 2 = 17). This gives us (4/30x^17).
Step 3: Simplify the result.
To fully simplify the expression, reduce the fractional coefficient (4/30) by dividing both the numerator and denominator by their greatest common divisor, which is 2. This results in (2/15x^17).
Therefore, the fully simplified expression, ignoring non-permissible values, is 2/15x^17.
So, the correct answer is option d) 2/15x^17.