Question

Which expression is equivalent to 14a^4b^6c^ -10/ 8a^ -2b^3c^ -5 please explain

A. 7a^2b^3/ 4c^15
B.6a^2b^9/c^15
C.7a^6b^3/4c^5
D.7b^2c^2/4a^2

Answer 1

To simplify the expression 14a^4b^6c^-10/ 8a^-2b^3c^-5, we can combine the like terms in the numerator and denominator and apply the rules of exponents. The simplified expression is 7a^6b^3/4c^5.

Step-by-step explanation:

To simplify the expression 14a^4b^6c^-10/ 8a^-2b^3c^-5, we can combine the like terms in the numerator and denominator. When we divide like terms with the same base, we subtract their exponents. So, for 'a' we subtract 4 from -2, for 'b' we subtract 6 from 3, and for 'c' we subtract -10 from -5.

After simplifying, we get (14/8) * a^(4-(-2)) * b^(6-3) * c^(-10-(-5)).

This further simplifies to (7/4) * a^6 * b^3 * c^(-5). Therefore, the expression is equivalent to option C: 7a^6b^3/4c^5.

Answer 2

answer is C
7a^6b^3/4c^5