Simplify the expression using exponent properties
c12d3 over c11d5e-3
To simplify the expression c^12d^3 / c^11d^5e^-3 using exponent properties, we start by combining the variables with the same base.
The expression can be rewritten as: (c^12 / c^11) * (d^3 / d^5) * (1 / e^3)
Next, using the property of dividing exponents with the same base, we subtract the exponent of the denominator from the exponent of the numerator:
= c^(12-11) * d^(3-5) * (1 / e^3)
Simplifying further, we have:
= c^1 * d^-2 * (1 / e^3)
Finally, since any number or variable raised to the power of 1 is equal to itself, and a negative exponent indicates division, we can rewrite the expression as:
= c * (1 / d^2) * (1 / e^3)
or,
= c / (d^2 * e^3)