Put the expressions in order from least to greatest.
1. 11^4 / 11^11
2. 1 / 11^-4
3. (11^-3)^-3
4. 11^5 · 11^2
Put the expressions in order from least to greatest.
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Put the expressions in order from least to greatest.
1. 11^4 / 11^11
2. 1 / 11^-4
3. (11^-3)^-3
4. 11^5 · 11^2
To compare the expressions and order them from least to greatest, let’s simplify each one step by step:
1. ( frac{11^4}{11^{11}} ): Using the properties of exponents, we get ( 11^{4-11} = 11^{-7} ).
2. ( frac{1}{11^{-4}} ): This can be rewritten as ( 11^{4} ) (because ( frac{1}{a^{-b}} = a^b )).
3. ( (11^{-3})^{-3} ): Again using the properties of exponents, we find ( 11^{-3 cdot -3} = 11^{9} ).
4. ( 11^5 cdot 11^2 ): Applying the product of powers rule gives ( 11^{5+2} = 11^{7} ).
Now, we can summarize the simplified expressions:
– ( 11^{-7} )
– ( 11^{4} )
– ( 11^{9} )
– ( 11^{7} )
Next, we can order the exponents from least to greatest:
– ( 11^{-7} ) (smallest)
– ( 11^{4} )
– ( 11^{7} )
– ( 11^{9} ) (largest)
Putting it all