To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

2b⁶ x 8b³
(2 x 8)b^{(6 + 3)}
16b⁹

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

8,736,000 in scientific notation is 8.736 x 10⁶

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{3}{100} \) x 7 = \( \frac{3 \times 7}{100} \) = \( \frac{21}{100} \) = 0.21 errors per hour

So, in an average hour, the machine will produce 7 - 0.21 = 6.79 error free parts.

The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 6.79 = 142.6 error free parts were produced yesterday.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{6 x 9}{5 x 9} \) + \( \frac{9 x 5}{9 x 5} \)

\( \frac{54}{45} \) + \( \frac{45}{45} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{54 + 45}{45} \) = \( \frac{99}{45} \) = 2\(\frac{1}{5}\)

If the tiger has consumed 80 pounds of food in 10 days that's \( \frac{80}{10} \) = 8 pounds of food per day. The tiger needs to consume 112 - 80 = 32 more pounds of food to reach 112 pounds total. At 8 pounds of food per day that's \( \frac{32}{8} \) = 4 more days.