6 over x to the 10th times x to the 17th over 51
To simplify the expression 6 / (x^10) * (x^17) / 51, we can use the properties of exponents and simplify each part separately before multiplying them together.
First, let's simplify the numerator, 6 * (x^17). Since we're multiplying two terms with the same base (x), we can add their exponents: 6 * x^(17+1) = 6 * x^18.
Next, let's simplify the denominator, (x^10) * 51. We can multiply these terms together: (x^10) * 51 = 51 * x^10.
Now, we can rewrite the expression as (6 * x^18) / (51 * x^10).
To divide two expressions with the same base (x), we subtract their exponents: x^18 / x^10 = x^(18-10) = x^8.
Finally, substituting this back into our expression, we have 6 / (51 * x^8).
So, the simplified expression is 6 / (51 * x^8).