1.
2p x 3p
Correct Answer
D. 6p^{2}
Explanation
Don'r forget to treat the numbers and letter separately
2.
Q x 4q x 5 q
Correct Answer
D. 20q^{3}
Explanation
The given expression consists of three terms: q, 4q, and 5q. The expression is then multiplied by q again, resulting in q * (q + 4q + 5q). Simplifying this further, we get q * 10q, which equals 10q^2. Finally, the expression 10q^2 is multiplied by 2, giving us the final answer of 20q^3.
3.
2p^{2} x 6p^{4}
Correct Answer
B. 12p^{6}
Explanation
The expression 2p2 x 6p4 represents the product of two permutations, with the first one having 2 elements and the second one having 6 elements. When we multiply permutations, we multiply the number of elements in each permutation. Therefore, 2p2 x 6p4 equals 2x6p2+4, which simplifies to 12p6.
4.
4a x 3a^{4}
Correct Answer
D. 12a^{5}
Explanation
The expression 4a x 3a4 can be simplified by multiplying the coefficients (4 and 3) to get 12, and combining the variables (a and a4) by adding their exponents, resulting in a5. Therefore, the simplified expression is 12a5.
5.
3n^{2} x 6n
Correct Answer
A. 18n^{3}
Explanation
The given expression is a multiplication of two terms, 3n^2 and 6n. To simplify the expression, we can multiply the coefficients, which gives us 3*6 = 18. Then, we can multiply the variables, n^2 * n = n^3. Combining these results, we get the simplified expression 18n^3.
6.
2b^{5} x 5b x 3b^{3}
Correct Answer
B. 30b^{9}
Explanation
The given expression involves multiplying three numbers: 2b5, 5b, and 3b3. When multiplying numbers with exponents, we add the exponents. Therefore, the product of 2b5 and 5b is 10b6, and when multiplied by 3b3, it becomes 30b9. Hence, the correct answer is 30b9.
7.
5m x 6n x n
Correct Answer
C. 30mn^{2}
Explanation
The given expression represents the product of three terms: 5m, 6n, and n. Multiplying these terms together gives 30mn^2, which is the same as the answer provided.
8.
3h^{2} x b^{3} x 4h^{3} x b^{4}
Correct Answer
D. 12h^{5}b^{7}
Explanation
The given expression consists of multiple terms being multiplied together. To simplify the expression, we need to multiply the coefficients and combine the variables with the same base. In this case, the coefficients are 3, 2, 4, and 4. When multiplied together, they give us 12. The variables consist of h and b, and we have h raised to the power of 2, h raised to the power of 3, b raised to the power of 3, and b raised to the power of 4. Combining the variables with the same base, we get h raised to the power of 5 and b raised to the power of 7. Therefore, the simplified expression is 12h5b7.
9.
4y^{2}z^{3} x 4y^{4}z^{5}
Correct Answer
D. 16y^{6}z^{8}
Explanation
The given expression is a multiplication of two terms: 4y2z3 and 4y4z5. When multiplying terms with the same base (y and z in this case), we add the exponents. Therefore, the y term becomes 2+4=6 and the z term becomes 3+5=8. The numerical coefficients, 4 and 4, are also multiplied to give 16. Thus, the correct answer is 16y6z8.
10.
5b^{3}a x 9ba^{2}
Correct Answer
C. 45b^{4}a^{3}
Explanation
The given question involves multiplying two numbers, 5b3a and 9ba2. To multiply these two numbers, we multiply the digits and then combine them according to their place values. The multiplication of 5 and 9 gives 45, the multiplication of b and b gives b^2, the multiplication of 3a and a2 gives 3a2, and the multiplication of 5b3a and 9ba2 gives 45b4a3. Therefore, the correct answer is 45b4a3.