With the restriction x ≠ 0, Which of the following is the simplified form of 6 times x to the ninth power over 4 times x to the fourth power times the fraction 12 times x to the fifth power over 3 times x squared ?

Question

campbell_st · Answer

you question is 


$$\frac{6x^9}{4x^4} \times \frac{12x^5}{2x^2}$$

the index law for division is subtract the powers

$$\frac{x^a}{x^b} = x^{a - b}$$

eliminate common factors with the integers

$$\frac{3}{2} x^{9 - 4} \times 6x^{5 - 2} = \frac{3}{2}x^5 \times 6 x^3$$

the index law for multiplication is add the powers

$$x^a \times x^b = x^{a + b}$$

multiply the numbers gives

$$9 x^{5 + 3} = 9x^8$$

hope this helps

anonymous · Answer

No wait the denominator of the second term is 3x^2 not 2x^2!

campbell_st · Answer

ok.... 12/3 = 4

and then its 3/2 * 4 = 6

so its 6 rather than 9

anonymous · Answer

Great! It was between 6x^8 and 6/x^8. Thank you!

campbell_st · Answer

it 6x^8