Solve 154/71:2a^3b*(-3ab)^3=

$$\frac { 154 } { 71 } : 2 a ^ { 3 } b \cdot ( - 3 a b ) ^ { 3 } =$$

Evaluate

$$-\frac{2079b^{4}a^{6}}{71}$$

Solution Steps

Express \frac{\frac{154}{71}}{2} as a single fraction.

$$\frac{154}{71\times 2}a^{3}b\left(-3ab\right)^{3}$$

Multiply 71 and 2 to get 142.

$$\frac{154}{142}a^{3}b\left(-3ab\right)^{3}$$

Reduce the fraction \frac{154}{142} to lowest terms by extracting and canceling out 2.

$$\frac{77}{71}a^{3}b\left(-3ab\right)^{3}$$

Expand \left(-3ab\right)^{3}.

$$\frac{77}{71}a^{3}b\left(-3\right)^{3}a^{3}b^{3}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{77}{71}a^{3}b\left(-27\right)a^{3}b^{3}$$

Multiply \frac{77}{71} and -27 to get -\frac{2079}{71}.

$$-\frac{2079}{71}a^{3}ba^{3}b^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$-\frac{2079}{71}a^{6}bb^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$-\frac{2079}{71}a^{6}b^{4}$$

Expand

$$-\frac{2079b^{4}a^{6}}{71}$$

Solution Steps

Express \frac{\frac{154}{71}}{2} as a single fraction.

$$\frac{154}{71\times 2}a^{3}b\left(-3ab\right)^{3}$$

Multiply 71 and 2 to get 142.

$$\frac{154}{142}a^{3}b\left(-3ab\right)^{3}$$

Reduce the fraction \frac{154}{142} to lowest terms by extracting and canceling out 2.

$$\frac{77}{71}a^{3}b\left(-3ab\right)^{3}$$

Expand \left(-3ab\right)^{3}.

$$\frac{77}{71}a^{3}b\left(-3\right)^{3}a^{3}b^{3}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{77}{71}a^{3}b\left(-27\right)a^{3}b^{3}$$

Multiply \frac{77}{71} and -27 to get -\frac{2079}{71}.

$$-\frac{2079}{71}a^{3}ba^{3}b^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$-\frac{2079}{71}a^{6}bb^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$-\frac{2079}{71}a^{6}b^{4}$$