Solve frac{(x^{3})^{2}}{6^5}*(6^2/6^4)^2)

$$\frac { ( x ^ { 3 } ) ^ { 2 } } { 6 ^ { 5 } } * ( \frac { 6 ^ { 2 } } { 6 ^ { 4 } } ) ^ { 2 } )$$

Evaluate

$$\frac{x^{6}}{10077696}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

Rewrite 6^{4} as 6^{2}\times 6^{2}. Cancel out 6^{2} in both numerator and denominator.

$$\frac{x^{6}}{6^{5}}\times \left(\frac{1}{6^{2}}\right)^{2}$$

Calculate 6 to the power of 5 and get 7776.

$$\frac{x^{6}}{7776}\times \left(\frac{1}{6^{2}}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{x^{6}}{7776}\times \left(\frac{1}{36}\right)^{2}$$

Calculate \frac{1}{36} to the power of 2 and get \frac{1}{1296}.

$$\frac{x^{6}}{7776}\times \frac{1}{1296}$$

Multiply \frac{x^{6}}{7776} times \frac{1}{1296} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{6}}{7776\times 1296}$$

Multiply 7776 and 1296 to get 10077696.

$$\frac{x^{6}}{10077696}$$

Expand

$$\frac{x^{6}}{10077696}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

Rewrite 6^{4} as 6^{2}\times 6^{2}. Cancel out 6^{2} in both numerator and denominator.

$$\frac{x^{6}}{6^{5}}\times \left(\frac{1}{6^{2}}\right)^{2}$$

Calculate 6 to the power of 5 and get 7776.

$$\frac{x^{6}}{7776}\times \left(\frac{1}{6^{2}}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{x^{6}}{7776}\times \left(\frac{1}{36}\right)^{2}$$

Calculate \frac{1}{36} to the power of 2 and get \frac{1}{1296}.

$$\frac{x^{6}}{7776}\times \frac{1}{1296}$$

Multiply \frac{x^{6}}{7776} times \frac{1}{1296} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{6}}{7776\times 1296}$$

Multiply 7776 and 1296 to get 10077696.

$$\frac{x^{6}}{10077696}$$