Evaluate (5^(1/2)*5^(-3/2))^(-1/4)

Math
(512⋅5-32)-14
Multiply 512 by 5-32 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
(512-32)-14
Combine the numerators over the common denominator.
(51-32)-14
Subtract 3 from 1.
(5-22)-14
Divide -2 by 2.
(5-1)-14
(5-1)-14
Multiply the exponents in (5-1)-14.
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Apply the power rule and multiply exponents, (am)n=amn.
5–14
Multiply –14.
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Multiply -1 by -1.
51(14)
Multiply 14 by 1.
514
514
514
The result can be shown in multiple forms.
Exact Form:
514
Decimal Form:
1.49534878…
Evaluate (5^(1/2)*5^(-3/2))^(-1/4)

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