Solve (3/9a^6b^2b^2)^3

$$( \frac { 3 } { 9 } a ^ { 6 } b ^ { 2 } b ^ { 2 } ) ^ { 3 }$$

Evaluate

$$\frac{b^{12}a^{18}}{27}$$

Solution Steps

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

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

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\left(\frac{1}{3}a^{6}b^{4}\right)^{3}$$

Expand \left(\frac{1}{3}a^{6}b^{4}\right)^{3}.

$$\left(\frac{1}{3}\right)^{3}\left(a^{6}\right)^{3}\left(b^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\left(\frac{1}{3}\right)^{3}a^{18}\left(b^{4}\right)^{3}$$

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

$$\left(\frac{1}{3}\right)^{3}a^{18}b^{12}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\frac{1}{27}a^{18}b^{12}$$

Expand

$$\frac{b^{12}a^{18}}{27}$$

Solution Steps

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

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

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\left(\frac{1}{3}a^{6}b^{4}\right)^{3}$$

Expand \left(\frac{1}{3}a^{6}b^{4}\right)^{3}.

$$\left(\frac{1}{3}\right)^{3}\left(a^{6}\right)^{3}\left(b^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\left(\frac{1}{3}\right)^{3}a^{18}\left(b^{4}\right)^{3}$$

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

$$\left(\frac{1}{3}\right)^{3}a^{18}b^{12}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\frac{1}{27}a^{18}b^{12}$$