Question

79. Use properties of exponents to rewrite each expression as either an integer or as a quotient of integers p/q to show the expression is a rational number.
b. 3√54/3√2

Answer 1

Answer:

See explanation below

Step-by-step explanation:

First we will going to rewrite 54 into its prime factors: 54 = 3³(2)

So, the expression $\frac{3\sqrt{54} }{3\sqrt{2} }$ can be written as:

$\frac{3\sqrt{3^32} }{3\sqrt{2} } =\frac{3(3^{3/2})2^{1/2} }{3(2^{1/2}) } =3^{3/2}=3\sqrt{3}$

*We used the fact that a  square root is like having a 1/2 exponent so we multiplied the exponents inside the root by 1/2 and then simplified them*