Solve [frac{(-3)^{2}(-4)^{3}7^-1}{3^5*5^2}]^3quadj

$$[ \frac { ( - 3 ) ^ { 2 } ( - 4 ) ^ { 3 } 7 ^ { - 1 } } { 3 ^ { 5 } \cdot 5 ^ { 2 } } ] ^ { 3 } \quad j$$

Evaluate

$$-\frac{262144j}{105488578125}$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$\left(\frac{9\left(-4\right)^{3}\times 7^{-1}}{3^{5}\times 5^{2}}\right)^{3}j$$

Calculate -4 to the power of 3 and get -64.

$$\left(\frac{9\left(-64\right)\times 7^{-1}}{3^{5}\times 5^{2}}\right)^{3}j$$

Multiply 9 and -64 to get -576.

$$\left(\frac{-576\times 7^{-1}}{3^{5}\times 5^{2}}\right)^{3}j$$

Calculate 7 to the power of -1 and get \frac{1}{7}.

$$\left(\frac{-576\times \frac{1}{7}}{3^{5}\times 5^{2}}\right)^{3}j$$

Multiply -576 and \frac{1}{7} to get -\frac{576}{7}.

$$\left(\frac{-\frac{576}{7}}{3^{5}\times 5^{2}}\right)^{3}j$$

Calculate 3 to the power of 5 and get 243.

$$\left(\frac{-\frac{576}{7}}{243\times 5^{2}}\right)^{3}j$$

Calculate 5 to the power of 2 and get 25.

$$\left(\frac{-\frac{576}{7}}{243\times 25}\right)^{3}j$$

Multiply 243 and 25 to get 6075.

$$\left(\frac{-\frac{576}{7}}{6075}\right)^{3}j$$

Express \frac{-\frac{576}{7}}{6075} as a single fraction.

$$\left(\frac{-576}{7\times 6075}\right)^{3}j$$

Multiply 7 and 6075 to get 42525.

$$\left(\frac{-576}{42525}\right)^{3}j$$

Reduce the fraction \frac{-576}{42525} to lowest terms by extracting and canceling out 9.

$$\left(-\frac{64}{4725}\right)^{3}j$$

Calculate -\frac{64}{4725} to the power of 3 and get -\frac{262144}{105488578125}.

$$-\frac{262144}{105488578125}j$$

Expand

$$-\frac{262144j}{105488578125}$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$\left(\frac{9\left(-4\right)^{3}\times 7^{-1}}{3^{5}\times 5^{2}}\right)^{3}j$$

Calculate -4 to the power of 3 and get -64.

$$\left(\frac{9\left(-64\right)\times 7^{-1}}{3^{5}\times 5^{2}}\right)^{3}j$$

Multiply 9 and -64 to get -576.

$$\left(\frac{-576\times 7^{-1}}{3^{5}\times 5^{2}}\right)^{3}j$$

Calculate 7 to the power of -1 and get \frac{1}{7}.

$$\left(\frac{-576\times \frac{1}{7}}{3^{5}\times 5^{2}}\right)^{3}j$$

Multiply -576 and \frac{1}{7} to get -\frac{576}{7}.

$$\left(\frac{-\frac{576}{7}}{3^{5}\times 5^{2}}\right)^{3}j$$

Calculate 3 to the power of 5 and get 243.

$$\left(\frac{-\frac{576}{7}}{243\times 5^{2}}\right)^{3}j$$

Calculate 5 to the power of 2 and get 25.

$$\left(\frac{-\frac{576}{7}}{243\times 25}\right)^{3}j$$

Multiply 243 and 25 to get 6075.

$$\left(\frac{-\frac{576}{7}}{6075}\right)^{3}j$$

Express \frac{-\frac{576}{7}}{6075} as a single fraction.

$$\left(\frac{-576}{7\times 6075}\right)^{3}j$$

Multiply 7 and 6075 to get 42525.

$$\left(\frac{-576}{42525}\right)^{3}j$$

Reduce the fraction \frac{-576}{42525} to lowest terms by extracting and canceling out 9.

$$\left(-\frac{64}{4725}\right)^{3}j$$

Calculate -\frac{64}{4725} to the power of 3 and get -\frac{262144}{105488578125}.

$$-\frac{262144}{105488578125}j$$