Algebra I

Here are some situations where quick shortcuts can save you a lot of time and help you avoid annoying arithmetic.


Simplify 23×2726×23.\large \frac{ {\color{#20A900}{2}} ^ {\color{#3D99F6}{3}} \times {\color{#20A900}{2}} ^ {\color{#3D99F6}{7}}}{ {\color{#20A900}{2}} ^ {\color{#3D99F6}{6}} \times {\color{#20A900}{2}} ^ {\color{#3D99F6}{3}} }.

Note: You are not a robot, and you don't need a calculator to solve this!

Exponent Shortcuts and Misconceptions

         

Which is larger,

34+34+34 or 35? \large 3 ^ { 4 } + 3 ^ { 4 } + 3 ^ { 4 } \hspace{.5cm} \text{ or } \hspace{.55cm} {3} ^ { 5} \, ?

Exponent Shortcuts and Misconceptions

         

Evaluate

4223824238. \large \frac{ \color{#3D99F6}{42} ^ 2 - \color{#20A900}{38} ^ 2 } { \color{#3D99F6}{42} - \color{#20A900}{38} }.

Hint: Use the difference of two squares identity: a2b2=(a+b)(ab) a^2-b^2=(a+b)(a-b).

Exponent Shortcuts and Misconceptions

         

What is the value of 282? \LARGE {\color{#3D99F6}{ 2}} ^ { {\color{#20A900}{8}} ^{ {\color{#3D99F6} { 2} }} } ?

Exponent Shortcuts and Misconceptions

         

At which step is the first error made in solving the equation given in Step 1?

Step 1. x+4=5\,\,\,\sqrt{x + 4} = 5

Step 2. x+4=5\,\,\,\sqrt{x} + \sqrt{4} = 5

Step 3. x+2=5\,\,\,\sqrt{x} + 2 = 5

Step 4. x=3\,\,\,\sqrt{x} = 3

Step 5. x=9\,\,\,x = 9

Exponent Shortcuts and Misconceptions

         
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