Question

I need this answer as soon as possible! 50 points!

Answer 1

Answer:

$800\sqrt{5}$

Step-by-step explanation:

Given: $\large (20)^ \dfrac{5}{2}$

Properties of Exponents:

Rational Exponent Property: $\large x^ \dfrac{m}{n} = \large \sqrt[n]{x^m}$

• a number raised to a fraction, can be converted to a radical.
• the numerator becomes the exponent, and the denominator becomes the index of the radical.

Product of Powers Property:

• when multiplying powers with the same base, add the exponents.

1. Convert into a radical:

$\sqrt[2]{20^5} \implies \sqrt{20^5}$

2. Simplify the expression:

$\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}$

3. Evaluate the power:

$20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}$

4. Multiply:

$(400\times2)\sqrt{5}\\\\\implies800\sqrt{5}$

Answer 2

$20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5$