(e) Express $$ \left(25^{\frac{1}{2}}\right)^{2} $$ in index form

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UpStudy AI · Accepted Answer

1. We start with the expression:
   $$
   \left(25^{\frac{1}{2}}\right)^{2}
   $$

2. Using the law of exponents $$\left(a^m\right)^n = a^{m \cdot n}$$, we multiply the exponents:
   $$
   \left(25^{\frac{1}{2}}\right)^{2} = 25^{\frac{1}{2} \cdot 2}
   $$

3. Multiply $$\frac{1}{2}$$ by $$2$$:
   $$
   \frac{1}{2} \times 2 = 1
   $$

4. So the expression simplifies to:
   $$
   25^1
   $$

5. In index form, $$25^1$$ is simply written as:
   $$
   25^1 \quad \text{or} \quad 25
   $$
$$25^1$$

(e) Express in index form

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