(5 2/3)^10 • (3/17)^10

To simplify the expression (5 2/3)^10 • (3/17)^10, we can start by converting the mixed number 5 2/3 to an improper fraction.

To convert 5 2/3 to an improper fraction, we multiply the whole number (5) by the denominator (3) and add the numerator (2). The denominator remains the same.

5 2/3 = (5 * 3 + 2)/3 = 17/3

Now, our expression becomes:

(17/3)^10 • (3/17)^10

Next, we can simplify each base raised to the power of 10 separately.

(17/3)^10 = (17^10)/(3^10)

(3/17)^10 = (3^10)/(17^10)

Now, our expression is:

(17^10)/(3^10) • (3^10)/(17^10)

Since the bases are the same, we can cancel them out, leaving us with:

1

Therefore, the simplified expression (5 2/3)^10 • (3/17)^10 is equal to 1.