1.
(x^{4})(x^{4})
Correct Answer
B. X^8
Explanation
The given expression is (x4)(x4), which means multiplying x raised to the power of 4 with x raised to the power of 4. When we multiply two exponents with the same base, we add their powers. Therefore, x^4 * x^4 is equal to x^(4+4), which simplifies to x^8.
2.
(-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 simplified as (-1)(x^3)(-1)(x^3). The two negative signs cancel each other out, leaving us with (x^3)(x^3) which can be further simplified as x^(3+3) = x^6. Therefore, the correct answer is x^6.
3.
A^{2}(a^{3})(a^{6})
Correct Answer
A. A^11
Explanation
The given expression consists of the variable 'a' raised to the powers 2, 3, and 6, which are multiplied together. To simplify this expression, we can add the exponents when multiplying like bases. Therefore, a^2 * a^3 * a^6 is equal to a^(2+3+6) which simplifies to a^11.
4.
X(x^{2})(x^{7})
Correct Answer
A. X^10
Explanation
The given expression is the product of x raised to the power of 2, x raised to the power of 7, and x itself. When multiplying powers with the same base, we add their exponents. Therefore, x^2 * x^7 * x^1 simplifies to x^(2+7+1), which is equal to x^10.
5.
(y^{2}z)(yz^{2})
Correct Answer
B. Y^3z^3
Explanation
The given expression is the product of (y2z) and (yz2), which can be simplified by multiplying the coefficients separately (y * y * y) and (z * z * z), resulting in y^3z^3. This is the correct answer because it represents the simplified form of the given expression.
6.
(cd^{2})(c^{3}d^{2})
Correct Answer
B. C^4d^4
Explanation
The given expression consists of two sets of parentheses. The first set, (cd2), means that we have c multiplied by d squared. The second set, (c3d2), means that we have c cubed multiplied by d squared. When we simplify the expression, we multiply the coefficients (c and c cubed) and add the exponents (d squared and d squared), resulting in c to the power of 4 and d to the power of 4. Therefore, the correct answer is c^4d^4.
7.
(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 combine the variables by adding the exponents: x^1 * x^3 = x^4 and y^3 * y^5 = y^8. Therefore, the simplified expression is 12x^4y^8.
8.
(-5m^{3})(3m^{8})
Correct Answer
C. -15m^11
Explanation
To simplify the expression (-5m^3)(3m^8), we multiply the coefficients (-5)(3) to get -15. Then, we multiply the variables with the same base, m, and add their exponents. The exponent of m in the first term is 3, and in the second term, it is 8. So, when we multiply the variables, we add 3 + 8, which equals 11. Therefore, the simplified expression is -15m^11.
9.
(10^{2})^{3}
Correct Answer
A. 10^6
Explanation
The given expression is (102)3. This means that 102 is raised to the power of 3. To simplify this expression, we need to multiply 102 by itself three times. Therefore, the correct answer is 10^6, which represents 102 multiplied by itself three times.
10.
(e^{2}f^{4})(e^{2}f^{2})
Correct Answer
C. E^4f^6
Explanation
The given expression is a product of two terms, (e2f4) and (e2f2). To simplify the expression, we can multiply the exponents of the common base, e, which gives us e^4. Similarly, we can multiply the exponents of the common base, f, which gives us f^6. Therefore, the simplified expression is e^4f^6.
11.
N^{9}/n^{5}
Correct Answer
C. N^4
Explanation
The correct answer is n^4 because when dividing n^9 by n^5, we subtract the exponents which gives us n^(9-5) = n^4.
12.
2n^{4}/n
Correct Answer
A. 2n^3
Explanation
The given expression is 2n^4/n. To simplify this expression, we can divide the numerator (2n^4) by the denominator (n). Dividing 2n^4 by n gives us 2n^3. Therefore, the correct answer is 2n^3.
13.
X^{3}y^{4}/x^{2}y
Correct Answer
C. Xy^3
Explanation
The given expression is a division of two terms, x3y4 and x2y. When dividing two terms with the same base (in this case, x), we subtract the exponents. So, we subtract 2 from 3, which gives us x3-2 = x^1 = x. Similarly, when dividing two terms with the same base (in this case, y), we subtract the exponents. So, we subtract 1 from 4, which gives us y4-1 = y^3. Therefore, the simplified expression is xy^3.
14.
20x^{3}y^{8}/-5x^{3}y
Correct Answer
B. -4y^7
Explanation
The given expression is a fraction with two terms in the numerator and one term in the denominator. To simplify the expression, we can cancel out common factors between the numerator and denominator. In this case, we can cancel out the common factors of "3y" from both terms in the numerator. After canceling out the common factors, we are left with "-4" in the numerator and "y" raised to the power of 7 in the denominator. Therefore, the simplified expression is -4y^7.
15.
3a^{5}b^{2}/9a^{2}b^{5}
Correct Answer
C. A^3/3b^3
Explanation
The given expression is a division of two terms. To simplify the expression, we can combine like terms and apply the rules of exponents. In the numerator, we have a^5 * b^2, and in the denominator, we have 9 * a^2 * b^5. By dividing the coefficients and subtracting the exponents of the variables, we get a^3 / (3b^3) as the simplified form of the expression.
16.
30a^{9}b^{2}/2a^{6}b^{2}
Correct Answer
B. 15a^3
Explanation
The given expression is a division problem, where 30a^9b^2 is divided by 2a^6b^2. When dividing like terms with the same base, we subtract the exponents. In this case, the common base is 'a'. The exponent of 'a' in the numerator is 9, and in the denominator, it is 6. Subtracting the exponents, we get a^3. The coefficient 15 remains unchanged. Therefore, the simplified expression is 15a^3, which is the correct answer.
17.
8u^{4}v^{10}/-2u^{2}v^{8}
Correct Answer
A. -4u^2v^2
Explanation
The given expression is a division of two terms: 8u^4v^10 and -2u^2v^8. When dividing two terms with the same base (u and v in this case), we subtract the exponents. Therefore, the expression simplifies to -4u^(4-2)v^(10-8), which further simplifies to -4u^2v^2.
18.
13u^{7}v^{7}/26u^{7}v
Correct Answer
C. V^6/2
Explanation
The given expression consists of terms with variables and exponents. Among the given options, only the term v^6/2 matches the given expression. Therefore, the correct answer is v^6/2.
19.
5^{5}/5^{2}
Correct Answer
A. 5^3
Explanation
The given expression is 55/52. The answer is 5^3. This means that 55/52 is equal to 5^3.
20.
A^{2}/a
Correct Answer
B. A
Explanation
The given expression is a2/a. When we divide a number by itself, the result is always 1. Therefore, a2/a simplifies to a.