QuestionAugust 25, 2025

Simplify. Your answer should contain only positive exponents that have been reduced. (1)/((sqrt (5))^-4) y^2 -(1)/(y^2) (1)/(y^2) -y^2

Simplify. Your answer should contain only positive exponents that have been reduced. (1)/((sqrt (5))^-4) y^2 -(1)/(y^2) (1)/(y^2) -y^2
Simplify. Your answer should contain only positive exponents that have been reduced. (1)/((sqrt (5))^-4) y^2 -(1)/(y^2) (1)/(y^2) -y^2

Solution
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Answer

25 Explanation 1. Simplify the expression with negative exponent The expression \frac{1}{(\sqrt{5})^{-4}} can be rewritten using the property of exponents: a^{-n} = \frac{1}{a^n}. Thus, (\sqrt{5})^{-4} = \frac{1}{(\sqrt{5})^4}. 2. Calculate the power of the square root (\sqrt{5})^4 = (5^{1/2})^4 = 5^{(1/2) \cdot 4} = 5^2 = 25. 3. Simplify the fraction Substitute back into the expression: \frac{1}{\frac{1}{25}} = 25.

Explanation

1. Simplify the expression with negative exponent<br /> The expression $\frac{1}{(\sqrt{5})^{-4}}$ can be rewritten using the property of exponents: $a^{-n} = \frac{1}{a^n}$. Thus, $(\sqrt{5})^{-4} = \frac{1}{(\sqrt{5})^4}$.<br /><br />2. Calculate the power of the square root<br /> $(\sqrt{5})^4 = (5^{1/2})^4 = 5^{(1/2) \cdot 4} = 5^2 = 25$.<br /><br />3. Simplify the fraction<br /> Substitute back into the expression: $\frac{1}{\frac{1}{25}} = 25$.
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