following. Express your answers i (b) quadroot(3)(25)×((1)/(sqrt125))^(-3)

Simplify Cube Root: We need to simplify the expression $ \sqrt[3]{25} \times \left(\frac{1}{\sqrt{125}}\right)^{-3} $. Let's start by simplifying each part separately.Simplify Fraction: First, we simplify $ \sqrt[3]{25} $. The cube root of 25 is not a whole number, but we can leave it in radical form as $ \sqrt[3]{25} $.Raise to Power: Next, we simplify $ \left(\frac{1}{\sqrt{125}}\right)^{-3} $. We know that $ \sqrt{125} = \sqrt{5^3} = 5 $, so $ \frac{1}{\sqrt{125}} = \frac{1}{5} $.Calculate Result: Now, we raise $ \frac{1}{5} $ to the power of -3, which is the same as taking the reciprocal and raising it to the power of 3: $ \left(\frac{1}{5}\right)^{-3} = 5^3 $.Multiply by Cube Root: Calculating $ 5^3 $ gives us $ 5 \times 5 \times 5 = 125 $.Final Answer: Now we multiply $ \sqrt[3]{25} $ by 125. Since we cannot simplify $ \sqrt[3]{25} $ further, the final answer is $ 125 \times \sqrt[3]{25} $.

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following. Express your answers i
(b)
quadroot(3)(25)×((1)/(sqrt125))^(-3)

following. Express your answers i $\newline$ (b) $\quad \sqrt[3]{25} \times\left(\frac{1}{\sqrt{125}}\right)^{-3}$

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Algebra 2

Sum of finite series starts from 1

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Q. following. Express your answers i

\newline

(b)

\quad \sqrt[3]{25} \times\left(\frac{1}{\sqrt{125}}\right)^{-3}

Simplify Cube Root: We need to simplify the expression $\sqrt[3]{25} \times \left(\frac{1}{\sqrt{125}}\right)^{-3}$ . Let's start by simplifying each part separately.
Simplify Fraction: First, we simplify $\sqrt[3]{25}$ . The cube root of $25$ is not a whole number, but we can leave it in radical form as $\sqrt[3]{25}$ .
Raise to Power: Next, we simplify $\left(\frac{1}{\sqrt{125}}\right)^{-3}$ . We know that $\sqrt{125} = \sqrt{5^3} = 5$ , so $\frac{1}{\sqrt{125}} = \frac{1}{5}$ .
Calculate Result: Now, we raise $\frac{1}{5}$ to the power of $-3$ , which is the same as taking the reciprocal and raising it to the power of $3$ : $\left(\frac{1}{5}\right)^{-3} = 5^3$ .
Multiply by Cube Root: Calculating $5^3$ gives us $5 \times 5 \times 5 = 125$ .
Final Answer: Now we multiply $\sqrt[3]{25}$ by $125$ . Since we cannot simplify $\sqrt[3]{25}$ further, the final answer is $125 \times \sqrt[3]{25}$ .