The question in the image asks to rewrite each expression as a single power (bilangan berpangkat). I'll solve each part individually:

a. $\sqrt{5} \cdot \sqrt{5}$

We can write square roots as fractional exponents:

$\sqrt{5} = 5^{\frac{1}{2}}$

Thus:

$\sqrt{5} \cdot \sqrt{5} = 5^{\frac{1}{2}} \cdot 5^{\frac{1}{2}} = 5^{\frac{1}{2} + \frac{1}{2}} = 5^1 = 5$

b. $\sqrt[3]{7} \cdot \sqrt[3]{7}$

Cube roots can be expressed as fractional exponents:

$\sqrt[3]{7} = 7^{\frac{1}{3}}$

Thus:

[ \sqrt[3]{7} \cdot \sqrt[3]{7} = 7^{\frac{1}{3}} \cdot 7^{\frac{1}{3}} = 7^{\frac{1}{3} + \frac{1}{3}} = 7^{\frac{2}{3}} ]

c. $\sqrt[5]{13} \cdot \sqrt[5]{13}$

Similarly:

$\sqrt[5]{13} = 13^{\frac{1}{5}}$

Thus:

[ \sqrt[5]{13} \cdot \sqrt[5]{13} = 13^{\frac{1}{5}} \cdot 13^{\frac{1}{5}} = 13^{\frac{2}{5}} ]

d. $\frac{\sqrt{3}}{\sqrt{3}}$

Since both numerator and denominator are the same, this simplifies to:

$\frac{\sqrt{3}}{\sqrt{3}} = 1$

e. $\frac{\sqrt[3]{7}}{\sqrt[7]{7}}$

Here we express the roots as exponents:

[ \sqrt[3]{7} = 7^{\frac{1}{3}}, \quad \sqrt[7]{7} = 7^{\frac{1}{7}} ]

Using the quotient rule for exponents:

$\frac{7^{\frac{1}{3}}}{7^{\frac{1}{7}}} = 7^{\frac{1}{3} - \frac{1}{7}} = 7^{\frac{7-3}{21}} = 7^{\frac{4}{21}}$

f. $\frac{\sqrt[5]{7}}{\sqrt[7]{7}}$

Again, expressing the roots as exponents:

[ \sqrt[5]{7} = 7^{\frac{1}{5}}, \quad \sqrt[7]{7} = 7^{\frac{1}{7}} ]

Using the quotient rule:

$\frac{7^{\frac{1}{5}}}{7^{\frac{1}{7}}} = 7^{\frac{1}{5} - \frac{1}{7}} = 7^{\frac{7-5}{35}} = 7^{\frac{2}{35}}$

Would you like any further details or clarification on these solutions?

Related Questions:

1. What is the general rule for multiplying terms with fractional exponents?
2. How do you simplify expressions involving both square and cube roots?
3. What is the rule for dividing exponents with the same base?
4. Can you explain the difference between a square root and a cube root?
5. How do you handle roots of roots, like $\sqrt{\sqrt{5}}$?

Tip:

When simplifying expressions with roots, always try to convert the roots into fractional exponents first, as it makes the operations of multiplication and division easier to handle.