Evaluate (-1/10)^3-(-1/10)^2-2*-1/10+1

Math
(-110)3-(-110)2-2⋅-110+1
Simplify each term.
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Move the negative in front of the fraction.
(-110)3-(-110)2-2⋅-110+1
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -110.
(-1)3(110)3-(-110)2-2⋅-110+1
Apply the product rule to 110.
(-1)313103-(-110)2-2⋅-110+1
(-1)313103-(-110)2-2⋅-110+1
Raise -1 to the power of 3.
-13103-(-110)2-2⋅-110+1
One to any power is one.
-1103-(-110)2-2⋅-110+1
Raise 10 to the power of 3.
-11000-(-110)2-2⋅-110+1
Move the negative in front of the fraction.
-11000-(-110)2-2⋅-110+1
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -110.
-11000-((-1)2(110)2)-2⋅-110+1
Apply the product rule to 110.
-11000-((-1)212102)-2⋅-110+1
-11000-((-1)212102)-2⋅-110+1
Multiply -1 by (-1)2 by adding the exponents.
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Move (-1)2.
-11000+(-1)2⋅-112102-2⋅-110+1
Multiply (-1)2 by -1.
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Raise -1 to the power of 1.
-11000+(-1)2⋅(-1)112102-2⋅-110+1
Use the power rule aman=am+n to combine exponents.
-11000+(-1)2+112102-2⋅-110+1
-11000+(-1)2+112102-2⋅-110+1
Add 2 and 1.
-11000+(-1)312102-2⋅-110+1
-11000+(-1)312102-2⋅-110+1
Raise -1 to the power of 3.
-11000-12102-2⋅-110+1
One to any power is one.
-11000-1102-2⋅-110+1
Raise 10 to the power of 2.
-11000-1100-2⋅-110+1
Cancel the common factor of 2.
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Factor 2 out of -2.
-11000-1100+2(-1)⋅-110+1
Factor 2 out of 10.
-11000-1100+2⋅-1⋅-12⋅5+1
Cancel the common factor.
-11000-1100+2⋅-1⋅-12⋅5+1
Rewrite the expression.
-11000-1100-1⋅-15+1
-11000-1100-1⋅-15+1
Move the negative in front of the fraction.
-11000-1100-1⋅(-15)+1
Multiply -1(-15).
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Multiply -1 by -1.
-11000-1100+1(15)+1
Multiply 15 by 1.
-11000-1100+15+1
-11000-1100+15+1
-11000-1100+15+1
To write -1100 as a fraction with a common denominator, multiply by 1010.
-11000-1100⋅1010+15+1
Write each expression with a common denominator of 1000, by multiplying each by an appropriate factor of 1.
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Multiply 1100 and 1010.
-11000-10100⋅10+15+1
Multiply 100 by 10.
-11000-101000+15+1
-11000-101000+15+1
Combine the numerators over the common denominator.
-1-101000+15+1
Subtract 10 from -1.
-111000+15+1
Find the common denominator.
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Multiply 15 by 200200.
-111000+15⋅200200+1
Combine.
-111000+1⋅2005⋅200+1
Write 1 as a fraction with denominator 1.
-111000+1⋅2005⋅200+11
Multiply 11 by 10001000.
-111000+1⋅2005⋅200+11⋅10001000
Multiply 11 and 10001000.
-111000+1⋅2005⋅200+10001000
Multiply 5 by 200.
-111000+1⋅2001000+10001000
-111000+1⋅2001000+10001000
Combine fractions.
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Combine fractions with similar denominators.
-11+1⋅200+10001000
Multiply 200 by 1.
-11+200+10001000
-11+200+10001000
Simplify the numerator.
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Add -11 and 200.
189+10001000
Add 189 and 1000.
11891000
11891000
The result can be shown in multiple forms.
Exact Form:
11891000
Decimal Form:
1.189
Mixed Number Form:
11891000
Evaluate (-1/10)^3-(-1/10)^2-2*-1/10+1

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