Question

Simplify the expression using the laws of exponents. 35a3b3c4 14a5b2c4 A) 5b 2a2 B) 5a2b 2 C) 5a2b 2 D) 5a3/5b3/2 2

Answer 1

The answer is A) (5b)/(2a²).


`(35a^3b^3c^4)/(14a^5b^2c^4)`

The coefficients are both divisible by 7, which gives us

`(5a^3b^3c^4)/(2a^5b^2c^4)`

The quotient rule for exponents says that when you divide powers, you subtract the exponents, and if the exponents are negative they go on the denominator. For a, the exponent will be 3-5=-2 (it will go on the denominator); for b, the exponent will be 3-2=1 (it will go on the numerator); and for c, the exponent will be 4-4=0 (c will effectively cancel out). This gives us


`(5b)/(2a^2)`