Solve (frac{30a^{7}b^{-9}c^{-3}}{5a^4b^-2c^2})^3

$$( \frac { 30 a ^ { 7 } b ^ { - 9 } c ^ { - 3 } } { 5 a ^ { 4 } b ^ { - 2 } c ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$\frac{216a^{9}}{c^{15}b^{21}}$$

Solution Steps

Cancel out 5a^{4} in both numerator and denominator.

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

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

$$\left(\frac{6a^{3}}{c^{5}b^{7}}\right)^{3}$$

To raise \frac{6a^{3}}{c^{5}b^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(6a^{3}\right)^{3}}{\left(c^{5}b^{7}\right)^{3}}$$

Expand \left(6a^{3}\right)^{3}.

$$\frac{6^{3}\left(a^{3}\right)^{3}}{\left(c^{5}b^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{6^{3}a^{9}}{\left(c^{5}b^{7}\right)^{3}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{216a^{9}}{\left(c^{5}b^{7}\right)^{3}}$$

Expand \left(c^{5}b^{7}\right)^{3}.

$$\frac{216a^{9}}{\left(c^{5}\right)^{3}\left(b^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{216a^{9}}{c^{15}\left(b^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{216a^{9}}{c^{15}b^{21}}$$

Expand

$$\frac{216a^{9}}{c^{15}b^{21}}$$

Solution Steps

Cancel out 5a^{4} in both numerator and denominator.

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

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

$$\left(\frac{6a^{3}}{c^{5}b^{7}}\right)^{3}$$

To raise \frac{6a^{3}}{c^{5}b^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(6a^{3}\right)^{3}}{\left(c^{5}b^{7}\right)^{3}}$$

Expand \left(6a^{3}\right)^{3}.

$$\frac{6^{3}\left(a^{3}\right)^{3}}{\left(c^{5}b^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{6^{3}a^{9}}{\left(c^{5}b^{7}\right)^{3}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{216a^{9}}{\left(c^{5}b^{7}\right)^{3}}$$

Expand \left(c^{5}b^{7}\right)^{3}.

$$\frac{216a^{9}}{\left(c^{5}\right)^{3}\left(b^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{216a^{9}}{c^{15}\left(b^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{216a^{9}}{c^{15}b^{21}}$$