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:

0.0008296 in scientific notation is 8.296 x 10^-4

If the tiger has consumed 35 pounds of food in 5 days that's \( \frac{35}{5} \) = 7 pounds of food per day. The tiger needs to consume 77 - 35 = 42 more pounds of food to reach 77 pounds total. At 7 pounds of food per day that's \( \frac{42}{7} \) = 6 more days.

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{10\sqrt{45}}{5\sqrt{9}} \)
\( \frac{10}{5} \) \( \sqrt{\frac{45}{9}} \)
2 \( \sqrt{5} \)

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:

-2a³ x 6a⁵
(-2 x 6)a^{(3 + 5)}
-12a⁸

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 30 meters so the equation becomes: 2w + 2h = 30.

Putting these two equations together and solving for width (w):

2w + 2h = 30
w + h = \( \frac{30}{2} \)
w + h = 15
w = 15 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 15 - 2w
3w = 15
w = \( \frac{15}{3} \)
w = 5

Since h = 2w that makes h = (2 x 5) = 10 and the area = h x w = 5 x 10 = 50 m²