Solve [(3a^{2}x^2+ax-4):(ax-1)-ax-4]^7:(2ax)^5-3(-ax)^2

$$[ ( 3 a ^ { 2 } x ^ { 2 } + a x - 4 ) : ( a x - 1 ) - a x - 4 ] ^ { 7 } : ( 2 a x ) ^ { 5 } - 3 ( - a x ) ^ { 2 }$$

Evaluate

$$\left(ax\right)^{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3a^{2}x^{2}+ax-4}{ax-1}.

$$\frac{\left(\frac{\left(3ax+4\right)\left(ax-1\right)}{ax-1}-ax-4\right)^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Cancel out ax-1 in both numerator and denominator.

$$\frac{\left(3ax+4-ax-4\right)^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Combine 3ax and -ax to get 2ax.

$$\frac{\left(2ax+4-4\right)^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Subtract 4 from 4 to get 0.

$$\frac{\left(2ax\right)^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Expand \left(2ax\right)^{7}.

$$\frac{2^{7}a^{7}x^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{128a^{7}x^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Expand \left(2ax\right)^{5}.

$$\frac{128a^{7}x^{7}}{2^{5}a^{5}x^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{128a^{7}x^{7}}{32a^{5}x^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Cancel out 32a^{5}x^{5} in both numerator and denominator.

$$4a^{2}x^{2}-3\left(\left(-a\right)x\right)^{2}$$

Expand \left(\left(-a\right)x\right)^{2}.

$$4a^{2}x^{2}-3\left(-a\right)^{2}x^{2}$$

Calculate -a to the power of 2 and get a^{2}.

$$4a^{2}x^{2}-3a^{2}x^{2}$$

Combine 4a^{2}x^{2} and -3a^{2}x^{2} to get a^{2}x^{2}.

$$a^{2}x^{2}$$

Expand

$$\left(ax\right)^{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3a^{2}x^{2}+ax-4}{ax-1}.

$$\frac{\left(\frac{\left(3ax+4\right)\left(ax-1\right)}{ax-1}-ax-4\right)^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Cancel out ax-1 in both numerator and denominator.

$$\frac{\left(3ax+4-ax-4\right)^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Combine 3ax and -ax to get 2ax.

$$\frac{\left(2ax+4-4\right)^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Subtract 4 from 4 to get 0.

$$\frac{\left(2ax\right)^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Expand \left(2ax\right)^{7}.

$$\frac{2^{7}a^{7}x^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{128a^{7}x^{7}}{\left(2ax\right)^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Expand \left(2ax\right)^{5}.

$$\frac{128a^{7}x^{7}}{2^{5}a^{5}x^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{128a^{7}x^{7}}{32a^{5}x^{5}}-3\left(\left(-a\right)x\right)^{2}$$

Cancel out 32a^{5}x^{5} in both numerator and denominator.

$$4a^{2}x^{2}-3\left(\left(-a\right)x\right)^{2}$$

Expand \left(\left(-a\right)x\right)^{2}.

$$4a^{2}x^{2}-3\left(-a\right)^{2}x^{2}$$

Calculate -a to the power of 2 and get a^{2}.

$$4a^{2}x^{2}-3a^{2}x^{2}$$

Combine 4a^{2}x^{2} and -3a^{2}x^{2} to get a^{2}x^{2}.

$$a^{2}x^{2}$$