Solve (3a^3)^2/(9a^-2)^2

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

Evaluate

$$\frac{a^{10}}{9}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

Expand \left(9a^{-2}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

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

Calculate 9 to the power of 2 and get 81.

$$\frac{9a^{6}}{81a^{-4}}$$

Cancel out 9 in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{a^{10}}{9}$$

Expand

$$\frac{a^{10}}{9}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

Expand \left(9a^{-2}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

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

Calculate 9 to the power of 2 and get 81.

$$\frac{9a^{6}}{81a^{-4}}$$

Cancel out 9 in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{a^{10}}{9}$$