Question

18........................

Answer 1

Answer:

D

Step-by-step explanation:

We will use the radical property  $\sqrt{a*b} =\sqrt{a} \sqrt{b}$  to simplify this.

The problem is  $\sqrt{169*x^5}$

We can simplify this as:

$\sqrt{169*x^5} \\=\sqrt{169} \sqrt{x^5}$

Now we can use the property of radicals,  $\sqrt[n]{x^a} =x^{\frac{a}{n}}$  , to write as:

$\sqrt{169} \sqrt{x^5} \\13*x^{\frac{5}{2}}$

D is right answer.

Answer 2

Answer:

d. $13x^{\frac{5}{2}}$

Step-by-step explanation:

The given expression is

$\sqrt{169x^5}$

We can rewrite this as

$\sqrt{169}\times \sqrt{x^5}$

We rewrite as a rational exponent to obtain;

$(13^2)^{\frac{1}{2}}\times (x^5)^{\frac{1}{2}}$

Recall that;

$(a^m)^n=a^{mn}$

$13^{(2\times \frac{1}{2})}\times (x)^{5\times \frac{1}{2}}$

$13^1 (x)^{\frac{5}{2}}$

The correct choice is D

$13x^{\frac{5}{2}}$