Question

15 POINTS

If x>0 and y>0, which expression is equivalent to 768x^19y^37

Answer 1

Answer:

Your answer is D.

Step-by-step explanation:

Answer 2

The expression which is equivalent to $\sqrt{768x^{19}y^{37}}$ is $16x^9y^{18}\sqrt{3xy}$.

What is the rule of exponent?

The Power rule for Exponents: $(a m)^{n} = a^{m*n}.$

To increase a number with an exponent to a power, multiply the exponent terms by the power.

In mathematics, power represents a base number increased to the exponent, where the base number exists as the factor which stands multiplied by itself and the exponent indicates the number of times the exact base number exists multiplied.

How to estimate the equivalent expression of $\sqrt{768x^{19}y^{37}}$?

Let, the given equation be $\sqrt{768x^{19}y^{37}}$ then

Separating the roots, we get

$\sqrt{768x^{19}y^{37}} = \sqrt{768}\sqrt{x^19}\sqrt{y^37}$

Simplifying the above equation, we get

$\sqrt{x^19} = x^9\sqrt{x}$

$=\sqrt{768}x^9\sqrt{x}\sqrt{y^37}$

$\sqrt{y^37} = y^{18} \sqrt{y}$

$=\sqrt{768}x^9\sqrt{x}y^{18}\sqrt{y}$

Equating the above equation,

$\sqrt{768} =16\sqrt{3}$

$= 16\sqrt{3}x^9\sqrt{x}y^{18}\sqrt{y}$

$= 16\sqrt{3}x^9y^{18}\sqrt{x}\sqrt{y}$

$= 16x^9y^{18}\sqrt{3xy}$

The expression which is equivalent to $\sqrt{768x^{19}y^{37}}$ is $16x^9y^{18}\sqrt{3xy}$.

Therefore, the correct answer is option D.$16x^9y^{18}\sqrt{3xy}$.

To learn more about property of exponent refer to:

https://brainly.com/question/3187898

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