To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-9x⁷ + 6x⁷
(-9 + 6)x⁷
-3x⁷

To simplify a radical, factor out the perfect squares:

\( \sqrt{125} \)
\( \sqrt{25 \times 5} \)
\( \sqrt{5^2 \times 5} \)
5\( \sqrt{5} \)

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.

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

\( \frac{9 x 7}{3 x 7} \) - \( \frac{5 x 3}{7 x 3} \)

\( \frac{63}{21} \) - \( \frac{15}{21} \)

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

\( \frac{63 - 15}{21} \) = \( \frac{48}{21} \) = 2\(\frac{2}{7}\)

If the tiger has consumed 18 pounds of food in 2 days that's \( \frac{18}{2} \) = 9 pounds of food per day. The tiger needs to consume 81 - 18 = 63 more pounds of food to reach 81 pounds total. At 9 pounds of food per day that's \( \frac{63}{9} \) = 7 more days.