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Let's begin by solving question 6(b), as requested.

### 6(b) Express \(\sqrt[3]{9} \div \sqrt[6]{3}\) in the form \( b \sqrt{15} \).

The expression is:
\[
\frac{\sqrt[3]{9}}{\sqrt[6]{3}}.
\]

We will follow these steps:
1. Rewrite \(\sqrt[3]{9}\) and \(\sqrt[6]{3}\) in terms of powers.
2. Simplify the powers.
3. Try to express the final result in the form \(b \sqrt{15}\).

#### Step 1: Rewrite the radicals as exponents

\[
\sqrt[3]{9} = 9^{1/3}, \quad \sqrt[6]{3} = 3^{1/6}.
\]

Next, express 9 as a power of 3:

\[
9 = 3^2, \quad \text{so} \quad \sqrt[3]{9} = (3^2)^{1/3} = 3^{2/3}.
\]

Now the expression becomes:

\[
\frac{3^{2/3}}{3^{1/6}}.
\]

#### Step 2: Simplify the expression

Using the law of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we subtract the exponents:

\[
3^{2/3 - 1/6}.
\]

To subtract these, first rewrite with a common denominator:

\[
2/3 = 4/6, \quad \text{so} \quad 3^{2/3 - 1/6} = 3^{(4/6 - 1/6)} = 3^{3/6} = 3^{1/2}.
\]

This simplifies to:

\[
3^{1/2} = \sqrt{3}.
\]

Thus, \(\frac{\sqrt[3]{9}}{\sqrt[6]{3}} = \sqrt{3}\).

#### Step 3: Express in the form \( b \sqrt{15} \)

Since \(\sqrt{3}\) does not involve 15, we cannot express it in the form \( b \sqrt{15} \). It seems there was an error in the form expected, and the correct simplified answer is:

\[
\sqrt{3}.
\]

If you'd like further clarification on how to approach similar problems or have any other questions, let me know!

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Would you like to explore another problem from the image? Here are five options related to this:

1. Solve question 7(a): Find expressions for \(x\) and \(2y\) in terms of \(t\).
2. Solve question 7(b): Find the value of \(t\) such that \(2y^2 - xy = 0\).
3. Solve question 8: Solve the equation involving \(\sqrt{2}(3x - 1) = 2(x + 3)\).
4. Solve question 9(a): Express \(6^{n+1} - 36^{n-2}\) in the form \(ax + b\).
5. Solve question 10(a): Express \( (3 - \sqrt{2})(1 + \sqrt{2}) \) in the form \(a + b\sqrt{2}\).

**Tip**: When dealing with radical expressions, converting them into fractional exponents often simplifies the operations and makes it easier to apply exponent rules.

Express √[3]{9} ÷ √[6]{3} in the form b√{15}.

Learn how to simplify the expression √[3]{9} ÷ √[6]{3} and express it in the form b√{15}. This problem covers radical simplifications, exponents, and exponent subtraction rules. Perfect for students in Grades 10-12.

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