First we should simplify the first expression. We can first apply the power of a product rule and then apply the power of a power rule. So we can write:

Return to the original expression:

Since the variables have the same exponents we can write:

Gina's mom baked 12 cookies; 8 were cinnamon and 4 were chocolate chip. If Gina then eats a cinnamon cookie, there will be 7 cinnamon cookies left.

After she eats the cookie, we need to find the difference between the number of cinnamon cookies and chocolate chip cookies.

There are 3 more cinnamon cookies than chocolate chip cookies.

In modulo 13 arithmetic, a number is congruent to the remainder of the divison of that number by 13. Since 

and 

,

, 

making the correct response 0.

By the order of operations, the operation within parentheses, which is addition, is carried out first; of the remaining two, multiplication precedes subtraction.

By the order of operations, in the absence of grouping symbols, exponentiation (squaring here) takes precedence, followed by, in order, multiplication and addition.

The algebraic way to solve this problem is to set up an equation, however, students can also solve using guess-and-check from the answer options.

When setting up an equation, sequential numbers are equal to , , , and . We know the sum of these sequential numbers to be 62, allowing us to set up the following equation:

Combine like-terms by reordering.

Subtract 6 from each side of the equation, then divide each side by 4 in order to isolate the variable.

In base five, each place value is a power of five, starting with 1 at the right, then, going to the left, 

To convert a base ten number to base five, divide the number by the next lowest power of five, then divide each remainder by progressively lower powers.

Since , we start by dividing 387 by 125, and continue accordingly:

The base five equivalent of 387 is 

If there are 3 students in each of Marie's art classes, and each student pays $15, this means that students are paying Marie $45 in total per class.

We can find the expense of the supplies by subtracting the amount Maria makes from the amount that the students pay her. The students pay her $45, but she only makes $35 per class.

The supplies must cost her $10.

Given that Joey's essay was 3 days late, he lost 15 points. This is because he loses 5 points for each day that it is late, and having turned it in 3 days late, lost 15 points. 

Joey's final score (68) will be equal to his original grade, minus the penalty.

If we add 15 to the score that ultimately received, the sum is 83.

If Joey had turned his essay in on time, he would have earned a score of 83. 

In base five, each place value is a power of five, starting with 1 at the right, then, going to the left, 

 can be calculated in base ten as

.