Question

now lets try raising a power to a power. write (10²)
expression\tfactors of the base\tsingle
(10²)³\t10²·10²·10²\t1
(10³)⁴\t10³·10³·10³·10³\t10
(10⁴)²\t10⁴·10⁴\t10
what is the relationship between the exponents? compl
(10⁴)² =
10⁴⁺²
√ 10⁴⁺²
10⁴⁻²
10⁴·²

Explanation:

Step1: Recall power of a power rule

For $(a^m)^n$, multiply exponents: $(a^m)^n = a^{m \cdot n}$

Step2: Apply rule to $(10^4)^2$

Substitute $a=10$, $m=4$, $n=2$: $(10^4)^2 = 10^{4 \cdot 2}$

Step3: Verify with factor expansion

$10^4 \cdot 10^4 = 10^{4+4} = 10^{8}$, and $4 \cdot 2 = 8$, so the correct form uses multiplication.

Answer:

$10^{4 \cdot 2}$ (the option $10^{4 \cdot 2}$)