Simplify the expression. $10 ^ { \sqrt { 10 } } \cdot 10 ^ { \sqrt { 10 } }$
A) $\quad 100 \sqrt { 20 }$
B) $\quad 100 \sqrt { 10 }$
C) $\quad 10 \sqrt { 20 }$
D) $\quad 20 \sqrt { 20 }$
E) $\quad 10 \sqrt { 10 }$

Question

Quizplus · Accepted Answer

The expression can be simplified using the property of exponents: $a^m \cdot a^n = a^{m+n}$. Here, $10^{\sqrt{10}} \cdot 10^{\sqrt{10}} = 10^{2\sqrt{10}}$. This is equivalent to $(10^{\sqrt{10}})^2$, which simplifies to $10^{2\sqrt{10}}$. This matches the form of $100\sqrt{10}$ since $10^{2\sqrt{10}}$ can be rewritten as $(10^{\sqrt{10}})^2 = (10^{\sqrt{10}} \cdot 10^{\sqrt{10}}) = 100^{\sqrt{10}}$.

Simplify the Expression 1010⋅101010 ^ { \sqrt { 10 } } \cdot 10 ^ { \sqrt { 10 } }1010​⋅1010​

Simplify the Expression $10 ^ { \sqrt { 10 } } \cdot 10 ^ { \sqrt { 10 } }$