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Simplify:
15.)
root(3)((64)/(729))

Simplify: $\newline$ $15$ .) $\sqrt[3]{\frac{64}{729}}$

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Multiplication with rational exponents

Full solution

Q. Simplify:

\newline

15

.)

\sqrt[3]{\frac{64}{729}}

Given Expression: We are given the expression $\sqrt[3]{\frac{64}{729}}$ , which means we need to find the cube root of the fraction $\frac{64}{729}$ . $\newline$ First, we will simplify the cube root of the numerator and the denominator separately.
Simplify Numerator: The cube root of the numerator is $\sqrt[3]{64}$ . $\newline$ Since $64$ is a perfect cube ( $4^3 = 64$ ), the cube root of $64$ is $4$ . $\newline$ $\sqrt[3]{64} = 4$
Simplify Denominator: The cube root of the denominator is $\sqrt[3]{729}$ . $\newline$ Since $729$ is a perfect cube ( $9^3 = 729$ ), the cube root of $729$ is $9$ . $\newline$ $\sqrt[3]{729} = 9$
Write Original Expression: Now we can write the original expression with the simplified cube roots: $\sqrt[3]{\frac{64}{729}} = \frac{\sqrt[3]{64}}{\sqrt[3]{729}}$ Substitute the simplified cube roots: $= \frac{4}{9}$
Final Simplified Form: The final simplified form of the expression is $\frac{4}{9}$ . There are no further simplifications needed, and there are no math errors.

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