Final answer:
The calculation of 100^-5 results in 10^-10, which equals 0.0000000001 because you move the decimal point to the left ten places when dividing by a power of ten with negative exponent.
Step-by-step explanation:
To calculate 100^-5, we need to understand what a negative exponent signifies. In general, a negative exponent indicates that the base number is to be divided into 1 that many times, effectively making it a fraction.
Therefore, 100-5 means we are dividing 1 by 100 five times, or (1/100)5. Since 100 is 102, this can be rewritten as (1/102)5. When we raise a power to a power, we multiply the exponents. This gives us 1/1010, which can be simplified to 10-10.
So, 100^-5 is equivalent to 10^-10. When dividing by powers of 10, you move the decimal to the left by the number of zeros in the power of ten. Therefore, 10-10 would be 0.0000000001.
To calculate 100^-5, we need to understand the concept of negative exponents. When a number is raised to a negative exponent, it is essentially being inverted. Therefore, 100^-5 is the same as 1/100^5. We can calculate this by multiplying 1 by 1/100 five times: 1/100 * 1/100 * 1/100 * 1/100 * 1/100. Using a calculator, this simplifies to 0.00000000001, or 1 x 10^-11.