Solve (-5)^2*|-1/5|-(-1/2)div(1/2)^2=

$$( - 5 ) ^ { 2 } \times | - \frac { 1 } { 5 } | - ( - \frac { 1 } { 2 } ) \div ( \frac { 1 } { 2 } ) ^ { 2 } =$$

Evaluate

$$7$$

Solution Steps

Calculate -5 to the power of 2 and get 25.

$$25|-\frac{1}{5}|-\frac{-\frac{1}{2}}{\left(\frac{1}{2}\right)^{2}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{5} is \frac{1}{5}.

$$25\times \frac{1}{5}-\frac{-\frac{1}{2}}{\left(\frac{1}{2}\right)^{2}}$$

Multiply 25 and \frac{1}{5} to get \frac{25}{5}.

$$\frac{25}{5}-\frac{-\frac{1}{2}}{\left(\frac{1}{2}\right)^{2}}$$

Divide 25 by 5 to get 5.

$$5-\frac{-\frac{1}{2}}{\left(\frac{1}{2}\right)^{2}}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$5-\frac{-\frac{1}{2}}{\frac{1}{4}}$$

Divide -\frac{1}{2} by \frac{1}{4} by multiplying -\frac{1}{2} by the reciprocal of \frac{1}{4}.

$$5-\left(-\frac{1}{2}\times 4\right)$$

Express -\frac{1}{2}\times 4 as a single fraction.

$$5-\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$5-\left(-2\right)$$

The opposite of -2 is 2.

$$5+2$$

Add 5 and 2 to get 7.

$$7$$

Factor

$$7$$