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:

-9a⁴ + 7a⁴
(-9 + 7)a⁴
-2a⁴

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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

9\( \sqrt{5} \) x 9\( \sqrt{8} \)
(9 x 9)\( \sqrt{5 \times 8} \)
81\( \sqrt{40} \)

Now we need to simplify the radical:

81\( \sqrt{40} \)
81\( \sqrt{10 \times 4} \)
81\( \sqrt{10 \times 2^2} \)
(81)(2)\( \sqrt{10} \)
162\( \sqrt{10} \)

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

\( \frac{18\sqrt{20}}{9\sqrt{4}} \)
\( \frac{18}{9} \) \( \sqrt{\frac{20}{4}} \)
2 \( \sqrt{5} \)

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

8b⁴ - 9b⁴
(8 - 9)b⁴
-b⁴