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:

-7z³ - 3z³
(-7 - 3)z³
-10z³

Christine scored 94% on the test meaning she earned 94% of the possible points on the test. There were 210 possible points on the test so she earned 210 x 0.94 = 198 points. Each question is worth 3 points so she got \( \frac{198}{3} \) = 66 questions right.

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

8\( \sqrt{63} \) - 6\( \sqrt{7} \)
8\( \sqrt{9 \times 7} \) - 6\( \sqrt{7} \)
8\( \sqrt{3^2 \times 7} \) - 6\( \sqrt{7} \)
(8)(3)\( \sqrt{7} \) - 6\( \sqrt{7} \)
24\( \sqrt{7} \) - 6\( \sqrt{7} \)

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

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{6} \) x \( \frac{1}{7} \) = \( \frac{1 x 1}{6 x 7} \) = \( \frac{1}{42} \) = \(\frac{1}{42}\)

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.