Chapter 11: Q. 163 (page 1069)

Show two different algebraic methods to simplify $4^{\frac{3}{2}}$ . Explain all your steps.

Short Answer

Expert verified

Simplify the expression with $a^{\frac{1}{n}}$ .
Simplify the expression with $a^{\frac{m}{n}}$ .
$4^{\frac{3}{2}} = 8$

Step by step solution

Step 1. Given Information

We are given an expression $4^{\frac{3}{2}}$ .

Step 2. Explanation

Simplify the expression with $a^{\frac{1}{n}} = \sqrt[n]{a}$ .

Simplify the expression with $a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$ .

$4^{\frac{3}{2}} = \sqrt[2]{4^{3}} 4^{\frac{3}{2}} = \sqrt[2]{64} 4^{\frac{3}{2}} = 8$

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Show two different algebraic methods to simplify $4^{\frac{3}{2}}$ . Explain all your steps.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Show two different algebraic methods to simplify $4^{\frac{3}{2}}$ . Explain all your steps.