The simplified form of the expression √( 45 x⁸ w⁷ ) is 3x⁴w³√(5w).
<h3>What is the simplified form of the expression?</h3>
Given the expression in the question;
√( 45 x⁸ w⁷ )
First, factor out 9 from 45
√( 9(5) x⁸ w⁷ )
√( 3²(5) x⁸ w⁷ )
Rewrite x⁸ as (x⁴)²
√( 3²(5) (x⁴)² w⁷ )
Rewrite w⁷ as ( w⁶ × w )
√( 3²(5) (x⁴)² ( w⁶ × w ) )
Rewrite w⁶ as (3³)²
√( 3²(5) (x⁴)² (w³)² × w )
We can now take the square roots of all the terms with a power of 2 and take them out of the square root
(3)(x⁴)(w³)√(5w)
3x⁴w³√(5w)
Therefore, the simplified form of the expression √( 45 x⁸ w⁷ ) is 3x⁴w³√(5w).
Learn more about exponent rule here: brainly.com/question/15993626
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