Solve [(15div5)^{4}]^{3}:[(2^{2}*5*3):12*2^5:2^4]^10-1^3

$$[ ( 15 \div 5 ) ^ { 4 } ] ^ { 3 } : [ ( 2 ^ { 2 } \times 5 \times 3 ) : 12 \cdot 2 ^ { 5 } : 2 ^ { 4 } ] ^ { 10 } - 1 ^ { 3 }$$

Evaluate

$$-\frac{9999468559}{10000000000}\approx -0.999946856$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{\left(\frac{15}{5}\right)^{12}}{\left(\frac{\frac{2^{2}\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Divide 15 by 5 to get 3.

$$\frac{3^{12}}{\left(\frac{\frac{2^{2}\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Calculate 3 to the power of 12 and get 531441.

$$\frac{531441}{\left(\frac{\frac{2^{2}\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{531441}{\left(\frac{\frac{4\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Multiply 4 and 5 to get 20.

$$\frac{531441}{\left(\frac{\frac{20\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Multiply 20 and 3 to get 60.

$$\frac{531441}{\left(\frac{\frac{60}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Divide 60 by 12 to get 5.

$$\frac{531441}{\left(\frac{5\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{531441}{\left(\frac{5\times 32}{2^{4}}\right)^{10}}-1^{3}$$

Multiply 5 and 32 to get 160.

$$\frac{531441}{\left(\frac{160}{2^{4}}\right)^{10}}-1^{3}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{531441}{\left(\frac{160}{16}\right)^{10}}-1^{3}$$

Divide 160 by 16 to get 10.

$$\frac{531441}{10^{10}}-1^{3}$$

Calculate 10 to the power of 10 and get 10000000000.

$$\frac{531441}{10000000000}-1^{3}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{531441}{10000000000}-1$$

Subtract 1 from \frac{531441}{10000000000} to get -\frac{9999468559}{10000000000}.

$$-\frac{9999468559}{10000000000}$$

Factor

$$-\frac{9999468559}{10000000000} = -0.9999468559$$