Solve 0.5^2*0.4^2*0.1/2+0.4*5*10^-3*10*y=

$$\frac { 0.5 ^ { 2 } \times 0.4 ^ { 2 } \times 0.1 } { 2 } + 0.4 \times 5 \times 10 ^ { - 3 } \times 10 \times y =$$

Evaluate

$$\frac{y}{50}+0.002$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and 1 to get -2.

$$\frac{0.5^{2}\times 0.4^{2}\times 0.1}{2}+0.4\times 5\times 10^{-2}y$$

Calculate 0.5 to the power of 2 and get 0.25.

$$\frac{0.25\times 0.4^{2}\times 0.1}{2}+0.4\times 5\times 10^{-2}y$$

Calculate 0.4 to the power of 2 and get 0.16.

$$\frac{0.25\times 0.16\times 0.1}{2}+0.4\times 5\times 10^{-2}y$$

Multiply 0.25 and 0.16 to get 0.04.

$$\frac{0.04\times 0.1}{2}+0.4\times 5\times 10^{-2}y$$

Multiply 0.04 and 0.1 to get 0.004.

$$\frac{0.004}{2}+0.4\times 5\times 10^{-2}y$$

Expand \frac{0.004}{2} by multiplying both numerator and the denominator by 1000.

$$\frac{4}{2000}+0.4\times 5\times 10^{-2}y$$

Reduce the fraction \frac{4}{2000} to lowest terms by extracting and canceling out 4.

$$\frac{1}{500}+0.4\times 5\times 10^{-2}y$$

Multiply 0.4 and 5 to get 2.

$$\frac{1}{500}+2\times 10^{-2}y$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{1}{500}+2\times \frac{1}{100}y$$

Multiply 2 and \frac{1}{100} to get \frac{1}{50}.

$$\frac{1}{500}+\frac{1}{50}y$$

Factor

$$\frac{10y+1}{500}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and 1 to get -2.

$$factor(\frac{0.5^{2}\times 0.4^{2}\times 0.1}{2}+0.4\times 5\times 10^{-2}y)$$

Calculate 0.5 to the power of 2 and get 0.25.

$$factor(\frac{0.25\times 0.4^{2}\times 0.1}{2}+0.4\times 5\times 10^{-2}y)$$

Calculate 0.4 to the power of 2 and get 0.16.

$$factor(\frac{0.25\times 0.16\times 0.1}{2}+0.4\times 5\times 10^{-2}y)$$

Multiply 0.25 and 0.16 to get 0.04.

$$factor(\frac{0.04\times 0.1}{2}+0.4\times 5\times 10^{-2}y)$$

Multiply 0.04 and 0.1 to get 0.004.

$$factor(\frac{0.004}{2}+0.4\times 5\times 10^{-2}y)$$

Expand \frac{0.004}{2} by multiplying both numerator and the denominator by 1000.

$$factor(\frac{4}{2000}+0.4\times 5\times 10^{-2}y)$$

Reduce the fraction \frac{4}{2000} to lowest terms by extracting and canceling out 4.

$$factor(\frac{1}{500}+0.4\times 5\times 10^{-2}y)$$

Multiply 0.4 and 5 to get 2.

$$factor(\frac{1}{500}+2\times 10^{-2}y)$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$factor(\frac{1}{500}+2\times \frac{1}{100}y)$$

Multiply 2 and \frac{1}{100} to get \frac{1}{50}.

$$factor(\frac{1}{500}+\frac{1}{50}y)$$

Factor out \frac{1}{500}.

$$\frac{1+10y}{500}$$