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

3\( \sqrt{4} \) x 3\( \sqrt{7} \)
(3 x 3)\( \sqrt{4 \times 7} \)
9\( \sqrt{28} \)

Now we need to simplify the radical:

9\( \sqrt{28} \)
9\( \sqrt{7 \times 4} \)
9\( \sqrt{7 \times 2^2} \)
(9)(2)\( \sqrt{7} \)
18\( \sqrt{7} \)

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $300
i = 0.07 x $300

No payments were made so the total amount due is the original amount + the accumulated interest:

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

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:

3a⁷ - 5a⁷
(3 - 5)a⁷
-2a⁷

To subtract these radicals together their radicands must be the same:

9\( \sqrt{18} \) - 9\( \sqrt{2} \)
9\( \sqrt{9 \times 2} \) - 9\( \sqrt{2} \)
9\( \sqrt{3^2 \times 2} \) - 9\( \sqrt{2} \)
(9)(3)\( \sqrt{2} \) - 9\( \sqrt{2} \)
27\( \sqrt{2} \) - 9\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them: