To simplify this expression, let's first rewrite the mixed number as an improper fraction:
2 7/9 = (2*9 + 7)/9 = 25/9
Now, substitute this back into the original expression:
(25/9)^9 * 3^19/5^15
Next, we can simplify the exponents by multiplying:
(25^9 / 9^9) * 3^19 / 5^15
Now, let's calculate the values of the individual terms:
25^9 = 19531259^9 = 3874204893^19 = 11622614675^15 = 30517578125
Finally, plug these values back into the expression:
(1953125 / 387420489) * 1162261467 / 30517578125
Now, multiply the fractions:
(1953125 1162261467) / (387420489 30517578125)
Calculating the numerator and denominator separately:
Numerator = 2264838399062500Denominator = 1180240701025396754282126875
Therefore, the final simplified value of the expression is:
2264838399062500 / 1180240701025396754282126875 = 0.00191733 (approx)
To simplify this expression, let's first rewrite the mixed number as an improper fraction:
2 7/9 = (2*9 + 7)/9 = 25/9
Now, substitute this back into the original expression:
(25/9)^9 * 3^19/5^15
Next, we can simplify the exponents by multiplying:
(25^9 / 9^9) * 3^19 / 5^15
Now, let's calculate the values of the individual terms:
25^9 = 1953125
9^9 = 387420489
3^19 = 1162261467
5^15 = 30517578125
Finally, plug these values back into the expression:
(1953125 / 387420489) * 1162261467 / 30517578125
Now, multiply the fractions:
(1953125 1162261467) / (387420489 30517578125)
Calculating the numerator and denominator separately:
Numerator = 2264838399062500
Denominator = 1180240701025396754282126875
Therefore, the final simplified value of the expression is:
2264838399062500 / 1180240701025396754282126875 = 0.00191733 (approx)