Final answer:
Gary's initial mistake was improperly multiplying the exponent by 4 instead of applying the correct operation to solve for e. Relevant math concepts include taking roots, handling powers of 10, and maintaining significant figures in calculations.
Step-by-step explanation:
The question concerns Gary's attempt to solve an equation, but it appears there is a mistake in his method. Gary started with the equation e to the power of 4 equals 2.5, and to solve for e, he multiplied both sides by 4 which resulted in an incorrect solution. The mistake is in the application of the power rules. When solving exponent equations, one should not multiply the exponent directly, but rather apply the appropriate mathematical operations such as taking the fourth root or using logarithms.
For problems that involve powers of 10, moving the decimal point is an effective way to handle them. For example, 1.6 × 10² translates to 160 and 2.4 × 10-2 to 0.024. Furthermore, when dealing with significant figures, the answer should reflect the precision of the given numbers. If the numbers provided have two significant figures, the final answer should also be in two significant figures, such as calculating the area A to be 4.5 m².
Understanding how to handle scientific notation calculations, including multiplying powers of 10 and maintaining significant figures is crucial. For instance, in scientific notation calculations like multiplying (4.506 × 10&sup4;) by (1.003 × 10²), we add the exponents to get 106.