Solve (6/x^2)^2*(3x^2)/(9x)^3

$$( \frac { 6 } { x ^ { 2 } } ) ^ { 2 } \cdot \frac { ( 3 x ^ { 2 } ) } { ( 9 x ) ^ { 3 } }$$

Evaluate

$$\frac{4}{27x^{5}}$$

Solution Steps

To raise \frac{6}{x^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(9x\right)^{3}.

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

Calculate 9 to the power of 3 and get 729.

$$\frac{6^{2}}{\left(x^{2}\right)^{2}}\times \frac{3x^{2}}{729x^{3}}$$

Cancel out 3x^{2} in both numerator and denominator.

$$\frac{6^{2}}{\left(x^{2}\right)^{2}}\times \frac{1}{243x}$$

Multiply \frac{6^{2}}{\left(x^{2}\right)^{2}} times \frac{1}{243x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6^{2}}{\left(x^{2}\right)^{2}\times 243x}$$

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

$$\frac{6^{2}}{x^{4}\times 243x}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{6^{2}}{x^{5}\times 243}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36}{x^{5}\times 243}$$

Expand

$$\frac{4}{27x^{5}}$$

Solution Steps

To raise \frac{6}{x^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(9x\right)^{3}.

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

Calculate 9 to the power of 3 and get 729.

$$\frac{6^{2}}{\left(x^{2}\right)^{2}}\times \frac{3x^{2}}{729x^{3}}$$

Cancel out 3x^{2} in both numerator and denominator.

$$\frac{6^{2}}{\left(x^{2}\right)^{2}}\times \frac{1}{243x}$$

Multiply \frac{6^{2}}{\left(x^{2}\right)^{2}} times \frac{1}{243x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6^{2}}{\left(x^{2}\right)^{2}\times 243x}$$

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

$$\frac{6^{2}}{x^{4}\times 243x}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{6^{2}}{x^{5}\times 243}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36}{x^{5}\times 243}$$