3%2F8)%5E1%2F2-x((2%2F5)%5E1%2F4)%5E1%2F2.jpeg "((2/5)3/8)^1/2 X((2/5)^1/4)^1/2")
Simplifying the Expression: ((2/5)<sup>3/8</sup>)<sup>1/2</sup> x ((2/5)<sup>1/4</sup>)<sup>1/2</sup>
This problem involves simplifying an expression with fractional exponents. Let's break it down step-by-step using the properties of exponents:
Key Properties of Exponents
- Power of a Power: (a<sup>m</sup>)<sup>n</sup> = a<sup>m*n</sup>
- Product of Powers: a<sup>m</sup> * a<sup>n</sup> = a<sup>m+n</sup>
Simplifying the Expression
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Apply the Power of a Power Property:
- ((2/5)<sup>3/8</sup>)<sup>1/2</sup> = (2/5)<sup>(3/8)*(1/2)</sup> = (2/5)<sup>3/16</sup>
- ((2/5)<sup>1/4</sup>)<sup>1/2</sup> = (2/5)<sup>(1/4)*(1/2)</sup> = (2/5)<sup>1/8</sup>
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Apply the Product of Powers Property:
- (2/5)<sup>3/16</sup> * (2/5)<sup>1/8</sup> = (2/5)<sup>(3/16) + (1/8)</sup>
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Simplify the Exponent:
- (2/5)<sup>(3/16) + (1/8)</sup> = (2/5)<sup>5/16</sup>
Therefore, the simplified expression is (2/5)<sup>5/16</sup>.