Solve a^9*a^5div(3a^4)^3

$$a ^ { 9 } \cdot a ^ { 5 } \div ( 3 a ^ { 4 } ) ^ { 3 }$$

Evaluate

$$\frac{a^{2}}{27}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 5 to get 14.

$$\frac{a^{14}}{\left(3a^{4}\right)^{3}}$$

Expand \left(3a^{4}\right)^{3}.

$$\frac{a^{14}}{3^{3}\left(a^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{a^{14}}{3^{3}a^{12}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{a^{14}}{27a^{12}}$$

Cancel out a^{12} in both numerator and denominator.

$$\frac{a^{2}}{27}$$

Expand

$$\frac{a^{2}}{27}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 5 to get 14.

$$\frac{a^{14}}{\left(3a^{4}\right)^{3}}$$

Expand \left(3a^{4}\right)^{3}.

$$\frac{a^{14}}{3^{3}\left(a^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{a^{14}}{3^{3}a^{12}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{a^{14}}{27a^{12}}$$

Cancel out a^{12} in both numerator and denominator.

$$\frac{a^{2}}{27}$$