a) 75:[(153-6.52).8+2023^0]
First, we need to simplify the expression inside the brackets:
(153-6.52).8+2023^0 = (146.48).8+1 = 117.184+1 = 118.184

Now, we can substitute this value back into the original expression:
75:118.184

To divide by a decimal number, we can multiply both the numerator and denominator by 1000 to get rid of the decimal:
(75*1000):(118.184*1000) = 75000:118184

This fraction cannot be simplified any further, so the final answer is:
75000:118184

b) 721+x=615+(-15)
To solve for x, we need to isolate it on one side of the equation. We can start by simplifying the right side of the equation:
615+(-15) = 600

Now, we can rewrite the equation as:
721+x = 600

To isolate x, we can subtract 721 from both sides of the equation:
721+x-721 = 600-721
x = -121

Therefore, the solution to the equation is x = -121.

c) 3^x3-9=2.3^2
To solve for x, we need to isolate it on one side of the equation. We can start by simplifying the right side of the equation:
2.3^2 = 2.9

Now, we can rewrite the equation as:
3^x3-9 = 2.9

To isolate x, we can add 9 to both sides of the equation:
3^x3-9+9 = 2.9+9
3^x3 = 11.9

To solve for x, we need to take the logarithm of both sides of the equation. Let's use the natural logarithm (ln):
ln(3^x3) = ln(11.9)

Using the logarithmic property, we can bring down the exponent:
x3 * ln(3) = ln(11.9)

Now, we can divide both sides of the equation by ln(3):
x3 = ln(11.9)/ln(3)

To solve for x, we need to take the cube root of both sides of the equation:
x = (ln(11.9)/ln(3))^(1/3)

Therefore, the solution to the equation is x = (ln(11.9)/ln(3))^(1/3).