A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

To simplify a radical, factor out the perfect squares:

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

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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:

0.0004975 in scientific notation is 4.975 x 10^-4

Monica scored 77% on the test meaning she earned 77% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.77 = 92 points. Each question is worth 4 points so she got \( \frac{92}{4} \) = 23 questions right.