Final answer:
The missing exponent when the base 10 is raised to reach 100,000 is 5. This is because 100,000 can be broken down to 10 × 10⁴, which combines to be 10⁵ when considering the law of exponents for the same base (10).
Step-by-step explanation:
The student asked to find the missing exponent when 10 is raised to a certain power to get 100,000. To solve this, we consider the power (exponent) of 10 to be equal to the number of places the decimal is moved to transform the original number into a digit term with one non-zero digit. For the number 100,000, we can write it in exponential form as 10 multiplied by itself a certain number of times until we reach 100,000.
Since 100,000 is 10 × 10,000 and we know that 10,000 is 10⁴ (because 10⁴ is 10 × 10 × 10 × 10 which is 10,000), we can say that 100,000 = 10 x 10⁴. Combining the base 10, it is actually 10⁵. Hence, the missing exponent is 5.
In general, remember that 10³ is 1,000 and as a sure-fire way, the concept of integer powers helps us understand that each power of 10 is 10 times the previous power. Therefore, for each additional power of 10, the number gains a zero when expressed in standard numerical form.