Question

question 12 of 60
write 30 as a product of prime factors.

question 13 of 60
write \\(\frac{5}{15}\\) in simplest form.

question 14 of 60
simplify.
\\(\frac{x^4}{x^6}\\)

question 15 of 60
simplify.
\\(\frac{54bc}{6abc}\\)

question 16 of 60
simplify.
\\(\frac{x^5}{x^2}\\)

Explanation:

Question 12

Step1: Start with the smallest prime

Divide 30 by 2 (the smallest prime number). $30\div2 = 15$

Step2: Divide the quotient by next prime

Divide 15 by 3 (the next prime number). $15\div3 = 5$

Step3: The last quotient is prime

5 is a prime number, so we stop here.

Step1: Find the GCD of numerator and denominator

The greatest common divisor (GCD) of 5 and 15 is 5.

Step2: Divide numerator and denominator by GCD

Divide both the numerator and the denominator by 5. $\frac{5\div5}{15\div5}=\frac{1}{3}$

Step1: Use the exponent rule for division

For $x^m\div x^n=x^{m - n}$, here $m = 4$ and $n = 6$. So $x^{4-6}=x^{-2}$

Step2: Rewrite with positive exponent

$x^{-2}=\frac{1}{x^{2}}$

Answer:

$30 = 2\times3\times5$

Question 13