Solve frac{(2x^{3})^{3}x(2^{2}x^{5})*5^{3}}{(5^{2})^2*2^3*(3*2^2)^2}

$$\frac { ( 2 x ^ { 3 } ) ^ { 3 } x ( 2 ^ { 2 } x ^ { 5 } ) \times 5 ^ { 3 } } { ( 5 ^ { 2 } ) ^ { 2 } \times 2 ^ { 3 } \times ( 3 \times 2 ^ { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{x^{15}}{180}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\left(2x^{3}\right)^{3}x^{6}\times 2^{2}\times 5^{3}}{\left(5^{2}\right)^{2}\times 2^{3}\times \left(3\times 2^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\left(2x^{3}\right)^{3}x^{6}\times 2^{2}\times 5^{3}}{5^{4}\times 2^{3}\times \left(3\times 2^{2}\right)^{2}}$$

Cancel out 2^{2}\times 5^{3} in both numerator and denominator.

$$\frac{x^{6}\times \left(2x^{3}\right)^{3}}{2\times 5\times \left(3\times 2^{2}\right)^{2}}$$

Expand \left(2x^{3}\right)^{3}.

$$\frac{x^{6}\times 2^{3}\left(x^{3}\right)^{3}}{2\times 5\times \left(3\times 2^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{x^{6}\times 2^{3}x^{9}}{2\times 5\times \left(3\times 2^{2}\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{x^{6}\times 8x^{9}}{2\times 5\times \left(3\times 2^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 9 to get 15.

$$\frac{x^{15}\times 8}{2\times 5\times \left(3\times 2^{2}\right)^{2}}$$

Multiply 2 and 5 to get 10.

$$\frac{x^{15}\times 8}{10\times \left(3\times 2^{2}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{15}\times 8}{10\times \left(3\times 4\right)^{2}}$$

Multiply 3 and 4 to get 12.

$$\frac{x^{15}\times 8}{10\times 12^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{x^{15}\times 8}{10\times 144}$$

Multiply 10 and 144 to get 1440.

$$\frac{x^{15}\times 8}{1440}$$

Divide x^{15}\times 8 by 1440 to get x^{15}\times \frac{1}{180}.

$$x^{15}\times \frac{1}{180}$$

Expand

$$\frac{x^{15}}{180}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\left(2x^{3}\right)^{3}x^{6}\times 2^{2}\times 5^{3}}{\left(5^{2}\right)^{2}\times 2^{3}\times \left(3\times 2^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\left(2x^{3}\right)^{3}x^{6}\times 2^{2}\times 5^{3}}{5^{4}\times 2^{3}\times \left(3\times 2^{2}\right)^{2}}$$

Cancel out 2^{2}\times 5^{3} in both numerator and denominator.

$$\frac{x^{6}\times \left(2x^{3}\right)^{3}}{2\times 5\times \left(3\times 2^{2}\right)^{2}}$$

Expand \left(2x^{3}\right)^{3}.

$$\frac{x^{6}\times 2^{3}\left(x^{3}\right)^{3}}{2\times 5\times \left(3\times 2^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{x^{6}\times 2^{3}x^{9}}{2\times 5\times \left(3\times 2^{2}\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{x^{6}\times 8x^{9}}{2\times 5\times \left(3\times 2^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 9 to get 15.

$$\frac{x^{15}\times 8}{2\times 5\times \left(3\times 2^{2}\right)^{2}}$$

Multiply 2 and 5 to get 10.

$$\frac{x^{15}\times 8}{10\times \left(3\times 2^{2}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{15}\times 8}{10\times \left(3\times 4\right)^{2}}$$

Multiply 3 and 4 to get 12.

$$\frac{x^{15}\times 8}{10\times 12^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{x^{15}\times 8}{10\times 144}$$

Multiply 10 and 144 to get 1440.

$$\frac{x^{15}\times 8}{1440}$$

Divide x^{15}\times 8 by 1440 to get x^{15}\times \frac{1}{180}.

$$x^{15}\times \frac{1}{180}$$