Question

Simplify the following expression: 21m^4⋅2n^3⋅2p^10÷3m^21⋅n^16⋅p^5

a. 14m^−17⋅n^−13⋅p^5
b. 14m^17⋅n^13⋅p^5
c. 73m^−17⋅n^−13⋅p^5
d. 7/3m^17⋅n^13⋅p^5

Answer 1

To simplify the given algebraic expression, multiply the coefficients, subtract the exponents for like bases, and write negative exponents as factors in the denominator, resulting in 14p^5/(m^17·n^13).

Step-by-step explanation:

To simplify the expression 21m^4·2n^3·2p^10÷3m^21·n^16·p^5, we will follow the laws of exponents and division of algebraic terms:

1. Multiply the coefficients (numerical parts) together and divide them by the coefficient in the denominator. In this case, (21·2·2)/3 = 14.
2. Subtract the exponents of the variables with the same base. For m: 4 - 21 = -17; for n: 3 - 16 = -13; and for p: 10 - 5 = 5.
3. Rewrite the expression with the new exponents. Negative exponents mean that the term is on the wrong side of the fraction line. Therefore, the terms with negative exponents will move to the denominator.

The simplified expression is 14m^-17·n^-13·p^5, which is written with positive exponents as 14p^5/(m^17·n^13). So, the correct choice is answer (a): 14m^-17·n^-13·p^5.