Solve 24a^4div(-3a)^2*4a^2

$$24 a ^ { 4 } \div ( - 3 a ) ^ { 2 } \times 4 a ^ { 2 }$$

Evaluate

$$\frac{32a^{4}}{3}$$

Solution Steps

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

$$\frac{24a^{4}}{\left(-3\right)^{2}a^{2}}\times 4a^{2}$$

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

$$\frac{24a^{4}}{9a^{2}}\times 4a^{2}$$

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

$$\frac{8a^{2}}{3}\times 4a^{2}$$

Express \frac{8a^{2}}{3}\times 4 as a single fraction.

$$\frac{8a^{2}\times 4}{3}a^{2}$$

Express \frac{8a^{2}\times 4}{3}a^{2} as a single fraction.

$$\frac{8a^{2}\times 4a^{2}}{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{8a^{4}\times 4}{3}$$

Multiply 8 and 4 to get 32.

$$\frac{32a^{4}}{3}$$

Expand

$$\frac{32a^{4}}{3}$$

Solution Steps

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

$$\frac{24a^{4}}{\left(-3\right)^{2}a^{2}}\times 4a^{2}$$

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

$$\frac{24a^{4}}{9a^{2}}\times 4a^{2}$$

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

$$\frac{8a^{2}}{3}\times 4a^{2}$$

Express \frac{8a^{2}}{3}\times 4 as a single fraction.

$$\frac{8a^{2}\times 4}{3}a^{2}$$

Express \frac{8a^{2}\times 4}{3}a^{2} as a single fraction.

$$\frac{8a^{2}\times 4a^{2}}{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{8a^{4}\times 4}{3}$$

Multiply 8 and 4 to get 32.

$$\frac{32a^{4}}{3}$$