1.
(4xy^{3})(3x^{3}y^{5})
Correct Answer
A. 12x^4y^8
Explanation
The given expression is a product of two terms, (4xy^3) and (3x^3y^5). To simplify the expression, we multiply the coefficients (4 and 3) to get 12. Then, we multiply the variables with the same base, x, by adding their exponents (1+3 = 4). Similarly, we multiply the variables with the same base, y, by adding their exponents (3+5 = 8). Therefore, the simplified expression is 12x^4y^8.
2.
(-5m^{3})(3m^{8})
Correct Answer
C. -15m^11
Explanation
The given expression is a multiplication of two terms: (-5m^3) and (3m^8). When multiplying two terms with the same base (m in this case), we add the exponents. Therefore, the exponent of m in the answer will be 3+8=11. The coefficient of the answer is obtained by multiplying the coefficients of the two terms, which is -5*3=-15. Therefore, the correct answer is -15m^11.
3.
(e^{2}f^{4})(e^{2}f^{2})
Correct Answer
C. E^4f^6
Explanation
The given expression can be simplified by multiplying the exponents of the common variables. In this case, the common variables are e and f. The exponents of e in the given terms are 2, 2, and 4. Adding these exponents gives us 8. Similarly, the exponents of f in the given terms are 4, 2, and 6. Adding these exponents gives us 12. Therefore, the simplified expression is e^8f^12. However, since the answer given is e^4f^6, it is not the correct answer.
4.
When a problem is asking to multiply two base numbers that are the same but have different exponents, what operation do I use for the exponents?
Correct Answer
A. Add
Explanation
When multiplying two base numbers with different exponents, the exponents are added. This is because when multiplying, you are essentially adding the same number (the base) repeatedly. The exponents indicate how many times the base is being multiplied by itself. Therefore, to find the product of the base numbers, the exponents are added together.
5.
4 x q x q x 5 x q = 20q^{3}
Correct Answer
A. True
Explanation
The given equation states that multiplying 4, q, q, 5, and q together results in 20q3. This equation is true because multiplying q by itself twice (q x q) gives q2, and multiplying it again by 4 gives 4q2. Then, multiplying 4q2 by 5 gives 20q2, and multiplying it by q once more gives 20q3. Therefore, the equation is true.
6.
3 x q x a x 5 x q = 35q^{2}a
Correct Answer
B. False
Explanation
The given equation states that 3 multiplied by q multiplied by a multiplied by 5 multiplied by q is equal to 35q2a. However, this is not true. The correct equation should be 15q2a, not 35q2a. Therefore, the answer is false.
7.
What is the solution to 3^{0}?
Correct Answer
1
8.
What is the solution to 2^{-3}?
Correct Answer
1/8
Explanation
The solution to 2-3 is -1. However, the given answer of 1/8 is incorrect.
9.
What is the solution to (x^{3})^{5}?
Correct Answer
x^15
Explanation
The expression (x^3)^5 can be simplified by applying the power of a power rule, which states that when raising a power to another power, you multiply the exponents. In this case, the exponent of x is 3, and it is raised to the power of 5. Multiplying these exponents gives us 15, so the solution is x^15.
10.
4 x q x q x 5 x q = 20q^{3}
Correct Answer
A. True
Explanation
The equation 4 x q x q x 5 x q = 20q3 is true. By simplifying the equation, we can see that 4 x q x q x 5 x q is equal to 20q^3. This means that multiplying q by itself three times and then multiplying it by 4 and 5 will result in 20q^3. Therefore, the answer is true.
11.
3 x q x a x 5 x q = 35q^{2}a
Correct Answer
B. False
Explanation
The given equation is 3 x q x a x 5 x q = 35q2a. However, when we simplify the equation, we get 15q2a, not 35q2a. Therefore, the given equation is not true and the correct answer is False.
12.
(x^{4})(x^{4})
Correct Answer
B. X^8
Explanation
The given expression consists of four terms, each of which is raised to the power of 4. When we have the same base raised to different exponents, we can simplify the expression by adding the exponents. In this case, since all the terms have the base "x" and are raised to the power of 4, we can add the exponents and get x^8 as the final answer.
13.
(-x^{3})(-x^{3})
Correct Answer
C. X^6
Explanation
When multiplying two negative numbers, the result is always positive. In this case, (-x3)(-x3) can be rewritten as (-1)(x^3)(-1)(x^3), which simplifies to x^3 * x^3. When multiplying like bases, we add the exponents, so x^3 * x^3 becomes x^(3+3) which is equal to x^6. Therefore, the correct answer is x^6.
14.
a^{2}(a^{3})(a^{6})
Correct Answer
A. A^11
Explanation
The given expression "a2(a3)(a6)" can be simplified by multiplying the exponents of the same base, which in this case is "a". So, a^2 multiplied by a^3 gives us a^5, and then a^5 multiplied by a^6 gives us a^11. Therefore, the correct answer is a^11.
15.
x(x^{2})(x^{7})
Correct Answer
A. X^10
Explanation
The given expression is a product of three terms, x, x^2, and x^7. When multiplying terms with the same base, we add their exponents. Therefore, x * x^2 * x^7 can be simplified to x^(1+2+7) = x^10.
16.
(y^{2}z)(yz^{2})
Correct Answer
B. Y^3z^3
Explanation
The given expression is a product of two terms, (y2z) and (yz2). To simplify the expression, we can multiply the coefficients (y and z) together, resulting in y^3z^3. This is the correct answer because when we multiply y^2 with y, we get y^3, and when we multiply z with z^2, we get z^3. Therefore, the simplified expression is y^3z^3.
17.
(cd^{2})(c^{3}d^{2})
Correct Answer
B. C^4d^4
Explanation
The given expression (cd2)(c3d2) can be simplified by multiplying the coefficients (c and d) and adding the exponents (2+3 and 2+2) separately. This results in c^5d^4. However, the answer provided is c^4d^4, which is incorrect.