Solve (a/2-0)^2(-1/2-6)^2

$$( \frac { a } { 2 } - 0 ) ^ { 2 } ( \frac { - 1 } { 2 } - 6 ) ^ { 2 }$$

Evaluate

$$\frac{169a^{2}}{16}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 0 times \frac{2}{2}.

$$\left(\frac{a}{2}-\frac{0\times 2}{2}\right)^{2}\left(\frac{-1}{2}-6\right)^{2}$$

Since \frac{a}{2} and \frac{0\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{a-0\times 2}{2}\right)^{2}\left(\frac{-1}{2}-6\right)^{2}$$

Do the multiplications in a-0\times 2.

$$\left(\frac{a}{2}\right)^{2}\left(\frac{-1}{2}-6\right)^{2}$$

To raise \frac{a}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{a^{2}}{2^{2}}\left(\frac{-1}{2}-6\right)^{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{a^{2}}{2^{2}}\left(-\frac{1}{2}-6\right)^{2}$$

Subtract 6 from -\frac{1}{2} to get -\frac{13}{2}.

$$\frac{a^{2}}{2^{2}}\left(-\frac{13}{2}\right)^{2}$$

Calculate -\frac{13}{2} to the power of 2 and get \frac{169}{4}.

$$\frac{a^{2}}{2^{2}}\times \frac{169}{4}$$

Multiply \frac{a^{2}}{2^{2}} times \frac{169}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a^{2}\times 169}{2^{2}\times 4}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{a^{2}\times 169}{4\times 4}$$

Multiply 4 and 4 to get 16.

$$\frac{a^{2}\times 169}{16}$$

Expand

$$\frac{169a^{2}}{16}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 0 times \frac{2}{2}.

$$\left(\frac{a}{2}-\frac{0\times 2}{2}\right)^{2}\left(\frac{-1}{2}-6\right)^{2}$$

Since \frac{a}{2} and \frac{0\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{a-0\times 2}{2}\right)^{2}\left(\frac{-1}{2}-6\right)^{2}$$

Do the multiplications in a-0\times 2.

$$\left(\frac{a}{2}\right)^{2}\left(\frac{-1}{2}-6\right)^{2}$$

To raise \frac{a}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{a^{2}}{2^{2}}\left(\frac{-1}{2}-6\right)^{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{a^{2}}{2^{2}}\left(-\frac{1}{2}-6\right)^{2}$$

Subtract 6 from -\frac{1}{2} to get -\frac{13}{2}.

$$\frac{a^{2}}{2^{2}}\left(-\frac{13}{2}\right)^{2}$$

Calculate -\frac{13}{2} to the power of 2 and get \frac{169}{4}.

$$\frac{a^{2}}{2^{2}}\times \frac{169}{4}$$

Multiply \frac{a^{2}}{2^{2}} times \frac{169}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a^{2}\times 169}{2^{2}\times 4}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{a^{2}\times 169}{4\times 4}$$

Multiply 4 and 4 to get 16.

$$\frac{a^{2}\times 169}{16}$$