Final answer:
The simplified form of the expression ((6⁻⁴)⁻⁹)/(6⁶) is 1.
Step-by-step explanation:
To simplify the expression ((6⁻⁴)⁻⁹)/(6⁶), we first simplify the exponents. To raise a number with a negative exponent to a positive exponent, we take the reciprocal of the base and the absolute value of the exponent. So, (6⁻⁴)⁻⁹ becomes (1/6⁴)⁹. Then, we simplify the expression by multiplying the numerators and denominators together. So, ((1/6⁴)⁹)/(6⁶) becomes 1/(6ⁿ), where n = 4 * 9 - 6 * 6.
To determine the value of n, we solve the equation n = 4 * 9 - 6 * 6. Simplifying, we get n = 36 - 36, which equals 0. Therefore, the simplified form of the expression ((6⁻⁴)⁻⁹)/(6⁶) is 1/(6⁰), which is equal to 1.
Learn more about Simplifying Exponents