Answer: [tex]2^4[/tex]
This is the same as writing 2^4
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Explanation:
The four copies of "2" in the denominator pair up with four copies of "2" in the numerator. Those pairs cancel out as shown below.
We're left with 4 copies of 2 multiplied together, which means:
[tex]2*2*2*2 = 2^4[/tex]
The exponent of 4 tells us how many copies of the base (2) are multiplied together.
Other examples:
[tex]5^3 = 5*5*5[/tex]
[tex]7^2 = 7*7[/tex]
[tex]10^4 = 10*10*10*10[/tex]
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Another approach:
We have 8 copies of "2" in the numerator. So the numerator condenses to [tex]2^8[/tex] while the denominator turns into [tex]2^4[/tex]
Then we use the exponent rule of [tex]\frac{a^b}{a^c} = a^{b-c}[/tex] to say the following
[tex]\frac{2^8}{2^4} = 2^{8-4} = 2^4[/tex]
Basically you subtract exponents. This rule only works when the bases are the same.
