Question

simplify the expression "the square root of x^10 times the square root of x^4" completely.
A. the square root of x^14
B. 2 times the square root of x^10
C. 3 times the square root of x^5
D. x^7

Answer 1

\[\sqrt{x ^{10}}\sqrt{x ^{4}}\]
This is an exponential mathematical expression, why exponential?
Radicals and exponents are both pretty much the same, the only difference is that a radical, respresents an exponent composed by a fraction.

We will use two properties to siplify the expression:
\[1) \sqrt{a}\sqrt{b}=\sqrt{ab}\]
\[2) a^x a^y = a ^{x+y}\]
The first one states that the product f two radicals is equal to the radical of the product of the radical numbers.
The second states that the product of two coeficents with diferent exponents is equal to the same coeficent to the power of the sum of the exponents x and y.

Having said that, let's apply the first one in order to obtain:
\[\sqrt{x ^{10}x^4}\]
And applying property 2) :
\[\sqrt{x ^{14}}\]

Answer 2

A