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Scilla [17]
2 years ago
14

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

Mathematics
2 answers:
hram777 [196]2 years ago
8 0

Answer:

800\sqrt{5}

Step-by-step explanation:

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

Properties of Exponents:

<u>Rational Exponent Property</u>: \large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \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.

<u>Product of Powers Property:</u>

  • 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}

IRINA_888 [86]2 years ago
3 0

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

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