https://file.aiquickdraw.com/mathbot/file/172589131022969pyfybh.jpg

Let's solve each of the given expressions step by step.

### Expression 3
\[
\sqrt[3]{20a^{10}b^{20}c^{9}}
\]
The cube root of a product is the product of the cube roots:
\[
\sqrt[3]{20a^{10}b^{20}c^{9}} = \sqrt[3]{20} \cdot a^{\frac{10}{3}} \cdot b^{\frac{20}{3}} \cdot c^{3}
\]
- \(\sqrt[3]{20}\) remains as is since it cannot be simplified further.
- \(a^{\frac{10}{3}}\) is \(a^{3\frac{1}{3}} \), meaning \(a^3\) and a cube root of \(a\).
- \(b^{\frac{20}{3}}\) simplifies to \(b^6b^{\frac{2}{3}}\).
- \(c^3\) simplifies to \(c^3\) because the exponent is a multiple of 3.

So,

Simplify the following algebraic radical expressions: (1) 3. \sqrt[3]{20a^{10}b^{20}c^{9}}, (2) 4. \sqrt[5]{\frac{486x^{17}y^{13}}{2050z^{18}}} \cdot 2\left(\sqrt[4]{\frac{16x^8}{y^{16}z^{20}}}\right), (3) 5. \sqrt[3]{\frac{680m^8}{n^{11}o^{16}}} \cdot \sqrt[3]{\frac{27o^{12}}{m^{11}}} \cdot 4m^3n^4

Explore the step-by-step process for simplifying complex radical expressions, including cube roots and fifth roots. This problem covers advanced algebra concepts such as exponents and radical expressions, perfect for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation