Lesson $$ 19 / \operatorname{sission} $$ a han How can you write $$ \left(10^{2}\right)^{2} $$ as a single power of 10 ? show your work.

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To write $$ \left(10^{2}\right)^{2} $$ as a single power of 10, we can use the property of exponents that states $$ (a^m)^n = a^{m \cdot n} $$.

Here are the steps:

1. Identify the base and the exponents in the expression $$ \left(10^{2}\right)^{2} $$.
   - Base: $$ 10 $$
   - Exponent: $$ 2 $$ (from $$ 10^2 $$) and $$ 2 $$ (the exponent outside the parentheses).

2. Apply the exponent rule:
   $$
   \left(10^{2}\right)^{2} = 10^{2 \cdot 2}
   $$

3. Calculate the new exponent:
   $$
   2 \cdot 2 = 4
   $$

4. Write the final expression:
   $$
   \left(10^{2}\right)^{2} = 10^{4}
   $$

Thus, $$ \left(10^{2}\right)^{2} $$ can be written as $$ 10^{4} $$.
$$ \left(10^{2}\right)^{2} = 10^{4} $$

Lesson \( 19 / \operatorname{sission} \) a han How can you write \( \left(10^{2}\right)^{2} \) as a single power of 10 ? show your work.

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