Answer:
For the expression you've given, (3/5)^(-3) ÷ (5/3)^5, first simplify the exponents and then calculate the reciprocal.
Explanation:
Here's the step-by-step process:
(3/5)^(-3) = (5/3)^3 (taking reciprocal of both sides)
(5/3)^5 = 5^5 / 3^5
Now the expression becomes:
(5/3)^3 ÷ (5^5 / 3^5)
Next, simplify the division by multiplying with the reciprocal of the second term:
(5/3)^3 * (3^5 / 5^5)
Now calculate the values:
(125/27) * (243 / 3125)
Multiply the numerators and denominators separately:
(125 * 243) / (27 * 3125)
Finally, calculate the result:
(30375) / (84375)
Now, to find the multiplicative inverse, take the reciprocal of the result:
1 / (30375 / 84375)
Which simplifies to:
84375 / 30375
So, the multiplicative inverse of the given expression is 28125/10125, which can be simplified to 75/27