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# Algebra Warmups

From cracking cryptograms to calculating the top speed of a rocket, algebra gives you tools to apply mathematical reasoning to a wide range of problems. Dive in and see what you already know!

\[ \Large \color{blue}{8} ^ { \color{red} {3} } \]

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

\[ \large \color{green}{2025} ^ { \color{purple} {0} } ? \]

Simplify

\[\large \frac{ \color{green}2 ^ \color{purple}{3} \times \color{green}2 ^ \color{purple}{7} } { \color{green}2 ^ {\color{purple}{6}} \times \color{green}2 ^ {\color{purple}{3}} }. \]

Which is larger:

\[ \large \color{blue}{2} ^ { 12} + \color{blue}{2} ^ { 12} \hspace{.5cm} \text{ OR } \hspace{.55cm} \color{blue}{2} ^ { 13} ? \]

What is the value of

\[ \LARGE \color{blue}{ 2} ^ { \color{green}{8} ^{ \color{blue} { 2} } } ? \]

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