Algebra
# Algebra Warmups

$\Large \color{#3D99F6}{8} ^ { \color{#D61F06} {3} }$

Exponents are shorthand notation for repeated multiplication.

Which of the following is equal to the number above?

Two rules of exponents are:

$\large a ^ 0 = 1 \text{ and } a ^ 1 = a.$

What is the value of

$\large \color{#20A900}{2025} ^ { \color{#69047E} {0} } ?$

Simplify

$\large \frac{ \color{#20A900}2 ^ {\color{#69047E}{3}} \times \color{#20A900}2 ^ \color{#69047E}{7} } { \color{#20A900}2 ^ {\color{#69047E}{6}} \times \color{#20A900}2 ^ {\color{#69047E}{3}} }.$

Which is larger:

$\large \color{#3D99F6}{2} ^ { 12} + \color{#3D99F6}{2} ^ { 12} \hspace{.5cm} \text{ OR } \hspace{.55cm} \color{#3D99F6}{2} ^ { 13} ?$

What is the value of

$\LARGE \color{#3D99F6}{ 2} ^ { \color{#20A900}{8} ^{ \color{#3D99F6} { 2} } } ?$