Solve (3a^3)^2div2a^4div(-3a)

$$( 3 a ^ { 3 } ) ^ { 2 } \div 2 a ^ { 4 } \div ( - 3 a )$$

Evaluate

$$-\frac{3a^{9}}{2}$$

Solution Steps

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

$$\frac{\frac{3^{2}\left(a^{3}\right)^{2}}{2}a^{4}}{-3a}$$

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

$$\frac{\frac{3^{2}a^{6}}{2}a^{4}}{-3a}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{9a^{6}}{2}a^{4}}{-3a}$$

Express \frac{9a^{6}}{2}a^{4} as a single fraction.

$$\frac{\frac{9a^{6}a^{4}}{2}}{-3a}$$

Express \frac{\frac{9a^{6}a^{4}}{2}}{-3a} as a single fraction.

$$\frac{9a^{6}a^{4}}{2\left(-3\right)a}$$

Cancel out 3a in both numerator and denominator.

$$\frac{3a^{4}a^{5}}{-2}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-3a^{4}a^{5}}{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{-3a^{9}}{2}$$

Expand

$$-\frac{3a^{9}}{2}$$

Solution Steps

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

$$\frac{\frac{3^{2}\left(a^{3}\right)^{2}}{2}a^{4}}{-3a}$$

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

$$\frac{\frac{3^{2}a^{6}}{2}a^{4}}{-3a}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{9a^{6}}{2}a^{4}}{-3a}$$

Express \frac{9a^{6}}{2}a^{4} as a single fraction.

$$\frac{\frac{9a^{6}a^{4}}{2}}{-3a}$$

Express \frac{\frac{9a^{6}a^{4}}{2}}{-3a} as a single fraction.

$$\frac{9a^{6}a^{4}}{2\left(-3\right)a}$$

Cancel out 3a in both numerator and denominator.

$$\frac{3a^{4}a^{5}}{-2}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-3a^{4}a^{5}}{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{-3a^{9}}{2}$$