Simplify this expression: #[(−1/2)^2]^3-:2^-3 ·(−1/2)^-4 -: 2^11 =#? Hint: #[(1/a)^n]^m= (1/a)^(n+m)# #a^j xx a^k = a^(j+k)# this true for all power expression so long they have the same base
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To simplify the given expression:
[ \left( \left( -\frac{1}{2} \right)^2 \right)^3 \div 2^{-3} \times \left( -\frac{1}{2} \right)^{-4} \div 2^{11} ]
We use the properties of exponents:
[ \left( \left( -\frac{1}{2} \right)^2 \right)^3 = \left( -\frac{1}{4} \right)^3 ]
[ \left( -\frac{1}{4} \right)^3 = -\frac{1}{64} ]
[ 2^{-3} = \frac{1}{2^3} = \frac{1}{8} ]
[ \left( -\frac{1}{2} \right)^{-4} = \frac{1}{\left( -\frac{1}{2} \right)^4} = \frac{1}{\frac{1}{16}} = 16 ]
[ 2^{11} = 2^{11} = 2048 ]
Now, we simplify:
[ \frac{-\frac{1}{64}}{\frac{1}{8}} \times 16 \div 2048 ]
[ = -\frac{1}{64} \times 8 \div 2048 ]
[ = -\frac{1}{8} \div 2048 ]
[ = -\frac{1}{8} \div 2048 ]
[ = -\frac{1}{16384} ]
So, the simplified expression is ( -\frac{1}{16384} ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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