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root(3)(-3)*((1)/(375))^((1)/(3))

$\sqrt[3]{-3} \cdot\left(\frac{1}{375}\right)^{\frac{1}{3}}$

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Multiplication with rational exponents

Full solution

Q.

\sqrt[3]{-3} \cdot\left(\frac{1}{375}\right)^{\frac{1}{3}}

Understand the Problem: Understand the problem. $\newline$ We need to simplify the expression which involves the cube root of $-3$ multiplied by the cube root of the reciprocal of $375$ .
Simplify $-3$ : Simplify the cube root of $-3$ . The cube root of $-3$ is simply $-3^{(1/3)}$ , which equals $-1.3$ because the cube root of a negative number is negative.
Simplify Reciprocal of $375$ : Simplify the cube root of the reciprocal of $375$ . $\newline$ First, we express $375$ as a product of its prime factors: $375 = 3 \times 5^3$ . $\newline$ Now, take the cube root of each factor: $(1/375)^{(1/3)} = (1/3)^{(1/3)} \times (1/5^3)^{(1/3)}$ . $\newline$ Simplify each term: $(1/3)^{(1/3)} \times (1/5) = 1/3^{(1/3)} \times 1/5$ .
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ Now we multiply $-1.3$ by $\frac{1}{3^{\frac{1}{3}}} \times \frac{1}{5}$ . $\newline$ So, the expression becomes: $-1 \times \frac{1}{3^{\frac{1}{3}}} \times \frac{1}{5}$ .
Simplify Expression: Simplify the expression. $\newline$ Multiplying the terms together, we get: $-\frac{1}{3^{\frac{1}{3}} \times 5}$ .
Check for Simplifications: Check for any possible simplifications. There are no further simplifications possible, as $3^{1/3}$ and $5$ are in their simplest form.

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