# Evaluate (2/5)^3+(1/10)^2-(1/2)^3

(25)3+(110)2-(12)3
Simplify each term.
Apply the product rule to 25.
2353+(110)2-(12)3
Raise 2 to the power of 3.
853+(110)2-(12)3
Raise 5 to the power of 3.
8125+(110)2-(12)3
Apply the product rule to 110.
8125+12102-(12)3
One to any power is one.
8125+1102-(12)3
Raise 10 to the power of 2.
8125+1100-(12)3
Apply the product rule to 12.
8125+1100-1323
One to any power is one.
8125+1100-123
Raise 2 to the power of 3.
8125+1100-18
8125+1100-18
To write 8125 as a fraction with a common denominator, multiply by 44.
8125⋅44+1100-18
To write 1100 as a fraction with a common denominator, multiply by 55.
8125⋅44+1100⋅55-18
Write each expression with a common denominator of 500, by multiplying each by an appropriate factor of 1.
Multiply 8125 and 44.
8⋅4125⋅4+1100⋅55-18
Multiply 125 by 4.
8⋅4500+1100⋅55-18
Multiply 1100 and 55.
8⋅4500+5100⋅5-18
Multiply 100 by 5.
8⋅4500+5500-18
8⋅4500+5500-18
Combine the numerators over the common denominator.
8⋅4+5500-18
Simplify the numerator.
Multiply 8 by 4.
32+5500-18
37500-18
37500-18
To write 37500 as a fraction with a common denominator, multiply by 22.
37500⋅22-18
To write -18 as a fraction with a common denominator, multiply by 125125.
37500⋅22-18⋅125125
Write each expression with a common denominator of 1000, by multiplying each by an appropriate factor of 1.
Multiply 37500 and 22.
37⋅2500⋅2-18⋅125125
Multiply 500 by 2.
37⋅21000-18⋅125125
Multiply 18 and 125125.
37⋅21000-1258⋅125
Multiply 8 by 125.
37⋅21000-1251000
37⋅21000-1251000
Combine the numerators over the common denominator.
37⋅2-1251000
Simplify the numerator.
Multiply 37 by 2.
74-1251000
Subtract 125 from 74.
-511000
-511000
Move the negative in front of the fraction.
-511000
The result can be shown in multiple forms.
Exact Form:
-511000
Decimal Form:
-0.051
Evaluate (2/5)^3+(1/10)^2-(1/2)^3

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