Solve (frac{a^{2}b^{3}c^{-3}}{a^-3b^4c^4})^3

$$( \frac { a ^ { 2 } b ^ { 3 } c ^ { - 3 } } { a ^ { - 3 } b ^ { 4 } c ^ { 4 } } ) ^ { 3 }$$

Evaluate

$$\frac{a^{15}}{b^{3}c^{21}}$$

Solution Steps

Cancel out b^{3} in both numerator and denominator.

$$\left(\frac{c^{-3}a^{2}}{a^{-3}bc^{4}}\right)^{3}$$

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

$$\left(\frac{c^{-3}a^{5}}{bc^{4}}\right)^{3}$$

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

$$\left(\frac{a^{5}}{bc^{7}}\right)^{3}$$

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

$$\frac{\left(a^{5}\right)^{3}}{\left(bc^{7}\right)^{3}}$$

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

$$\frac{a^{15}}{\left(bc^{7}\right)^{3}}$$

Expand \left(bc^{7}\right)^{3}.

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

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

$$\frac{a^{15}}{b^{3}c^{21}}$$

Expand

$$\frac{a^{15}}{b^{3}c^{21}}$$

Solution Steps

Cancel out b^{3} in both numerator and denominator.

$$\left(\frac{c^{-3}a^{2}}{a^{-3}bc^{4}}\right)^{3}$$

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

$$\left(\frac{c^{-3}a^{5}}{bc^{4}}\right)^{3}$$

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

$$\left(\frac{a^{5}}{bc^{7}}\right)^{3}$$

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

$$\frac{\left(a^{5}\right)^{3}}{\left(bc^{7}\right)^{3}}$$

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

$$\frac{a^{15}}{\left(bc^{7}\right)^{3}}$$

Expand \left(bc^{7}\right)^{3}.

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

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

$$\frac{a^{15}}{b^{3}c^{21}}$$