1.
P^{5} x p^{2}
Correct Answer
B. P^{7}
Explanation
Add the powers together!
2.
M^{2} x m^{8}
Correct Answer
C. M^{10}
Explanation
The given expression is a multiplication of two variables, m2 and m8. The answer, m10, is obtained by multiplying the variables together.
3.
B^{6} x b^{3}
Correct Answer
D. B^{9}
Explanation
The given expression is multiplying b6 with b3. When multiplying variables with the same base, you add the exponents. In this case, the exponent of b6 is 6 and the exponent of b3 is 3. Therefore, the product of b6 x b3 is b9.
4.
G^{4} x g
Correct Answer
B. G^{5}
Explanation
The given answer, g5, is the correct choice because it is the only option that is listed in the given set of options. The other options, g4, g3, and g2, are also listed in the set, but g5 is the only option that is not duplicated. Therefore, g5 is the unique and correct answer.
5.
H^{5} x h^{3} x h^{7}
Correct Answer
A. H^{15}
Explanation
The given expression "h5 x h3 x h7" represents the product of three variables: h5, h3, and h7. The answer "h15" can be obtained by multiplying the corresponding values of h5, h3, and h7, which results in 5 x 3 x 7 = 105. Therefore, the correct answer is h15.
6.
J^{4} x j^{2} x j
Correct Answer
C. J^{7}
Explanation
The answer "j7" is the correct one because it is the only option that follows the pattern of the given sequence. Each row in the sequence consists of three letters, and the middle letter is always "j". The first and third letters follow a pattern where they increase by 2 each time. In the last row, the first letter is "j" and the third letter is "5", so the missing letter should be "7" to maintain the pattern.
7.
Y^{2} x y^{3} x b^{4} x b^{5}
Correct Answer
D. Y^{5}b^{9}
Explanation
The given sequence consists of the multiplication of various numbers and letters. To find the correct answer, we need to multiply y by y to get y2, then multiply y2 by y3 to get y6, then multiply y6 by b4 to get y6b16, and finally multiply y6b16 by b5 to get y5b9. Therefore, the correct answer is y5b9.
8.
H^{4} x h^{5} x k^{3} x k
Correct Answer
C. H^{9}k^{4}
Explanation
The given expression consists of the variables h and k, along with their respective exponents. To simplify the expression, we need to multiply the coefficients and add the exponents of the variables with the same base. In this case, we have h raised to the power of 9 and k raised to the power of 4. Therefore, the correct answer is h9k4.
9.
G^{5} x g^{-3}
Correct Answer
D. G^{2}
Explanation
The given expression, g5 x g-3, represents the product of g raised to the power of 5 and g raised to the power of -3. When multiplying variables with the same base, you add their exponents. Therefore, g5 x g-3 simplifies to g(5 + -3) which is equal to g2.
10.
F^{-3} x f^{-4}
Correct Answer
C. F^{-7}
Explanation
The given expression is f-3 x f-4. To multiply two negative exponents, we add the exponents and keep the base the same. So, f-3 x f-4 can be simplified as f-7. Therefore, the correct answer is f-7.