Solve (frac{2a^{2}b^-3*b^0}{b^3})^3

$$( \frac { 2 a ^ { 2 } b ^ { - 3 } \cdot b ^ { 0 } } { b ^ { 3 } } ) ^ { 3 }$$

Evaluate

$$\frac{8a^{6}}{b^{18}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and 0 to get -3.

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

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

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

To raise \frac{2a^{2}}{b^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{\left(2a^{2}\right)^{3}}{b^{18}}$$

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

$$\frac{2^{3}\left(a^{2}\right)^{3}}{b^{18}}$$

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

$$\frac{2^{3}a^{6}}{b^{18}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8a^{6}}{b^{18}}$$

Expand

$$\frac{8a^{6}}{b^{18}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and 0 to get -3.

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

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

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

To raise \frac{2a^{2}}{b^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{\left(2a^{2}\right)^{3}}{b^{18}}$$

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

$$\frac{2^{3}\left(a^{2}\right)^{3}}{b^{18}}$$

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

$$\frac{2^{3}a^{6}}{b^{18}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8a^{6}}{b^{18}}$$