https://file.aiquickdraw.com/mathbot/file/1729471671914bmon7l9x.jpg

The expression in the image appears to be:

\[
\left( \sqrt[3]{k^6} \right) \left( \sqrt[3]{36k^8} \right)
\]

Let's simplify this step by step.

### Step 1: Simplify each cube root
We can simplify the cube roots of each term.

#### First term: \(\sqrt[3]{k^6}\)
Using the property \(\sqrt[n]{x^m} = x^{\frac{m}{n}}\), we get:
\[
\sqrt[3]{k^6} = k^{6/3} = k^2
\]

#### Second term: \(\sqrt[3]{36k^8}\)
We can break this into two parts:
\[
\sqrt[3]{36k^8} = \sqrt[3]{36} \times \sqrt[3]{k^8}
\]
- \(\sqrt[3]{36}\) is a constant. The cube root of 36 is approximately \(36^{1/3}\).
- \(\sqrt[3]{k^8} = k^{8/3}\).

So the second term becomes:
\[
36^{1/3} \times k^{8/3}
\]

### Step 2: Multiply the simplified terms
Now multiply the simplified forms of the two expressions:
\[
(k^2) \times \left( 36^{1/3} \times k^{8/3} \right)
\]
Using the property \(k^a \times k^b = k^{a+b}\), this becomes:
\[
36^{1/3} \times k^{2 + 8/3} = 36^{1/3} \times k^{6/3 + 8/3} = 36^{1/3} \times k^{14/3}
\]

Thus, the simplified expression is:
\[
36^{1/3} \times k^{14/3}
\]

Would you like more details on any part of this process or have any questions?

### 5 related questions:
1. How do you calculate cube roots of larger numbers like 36?
2. How do you handle cube roots of variables with higher exponents?
3. Can this expression be further simplified with approximation?
4. What are the general rules for multiplying terms with fractional exponents?
5. How would this expression change if the roots were square instead of cube?

**Tip**: When simplifying cube roots, remember that \(x^{m/n}\) is a general way to handle roots, where \(n\) is the root and \(m\) is the exponent.

Simplify the expression (√³(k^6))(√³(36k^8)).

Learn how to simplify the expression (√³(k^6))(√³(36k^8)) step by step. This solution involves understanding cube roots, exponents, and algebraic multiplication. Suitable for high school students (Grades 9-12).

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