Solve (frac{1a^{-2}b^{-3}c^{2}}{2a^-1b^-5c^-3})^3

$$( \frac { 1 a ^ { - 2 } b ^ { - 3 } c ^ { 2 } } { 2 a ^ { - 1 } b ^ { - 5 } c ^ { - 3 } } ) ^ { 3 }$$

Evaluate

$$\frac{b^{6}c^{15}}{8a^{3}}$$

Solution Steps

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

$$\left(\frac{a^{-2}b^{2}c^{5}}{2\times \frac{1}{a}}\right)^{3}$$

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

$$\left(\frac{b^{2}c^{5}}{2a^{1}}\right)^{3}$$

Calculate a to the power of 1 and get a.

$$\left(\frac{b^{2}c^{5}}{2a}\right)^{3}$$

To raise \frac{b^{2}c^{5}}{2a} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{2}c^{5}\right)^{3}}{\left(2a\right)^{3}}$$

Expand \left(b^{2}c^{5}\right)^{3}.

$$\frac{\left(b^{2}\right)^{3}\left(c^{5}\right)^{3}}{\left(2a\right)^{3}}$$

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

$$\frac{b^{6}\left(c^{5}\right)^{3}}{\left(2a\right)^{3}}$$

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

$$\frac{b^{6}c^{15}}{\left(2a\right)^{3}}$$

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

$$\frac{b^{6}c^{15}}{2^{3}a^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{b^{6}c^{15}}{8a^{3}}$$

Expand

$$\frac{b^{6}c^{15}}{8a^{3}}$$

Solution Steps

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

$$\left(\frac{a^{-2}b^{2}c^{5}}{2\times \frac{1}{a}}\right)^{3}$$

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

$$\left(\frac{b^{2}c^{5}}{2a^{1}}\right)^{3}$$

Calculate a to the power of 1 and get a.

$$\left(\frac{b^{2}c^{5}}{2a}\right)^{3}$$

To raise \frac{b^{2}c^{5}}{2a} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{2}c^{5}\right)^{3}}{\left(2a\right)^{3}}$$

Expand \left(b^{2}c^{5}\right)^{3}.

$$\frac{\left(b^{2}\right)^{3}\left(c^{5}\right)^{3}}{\left(2a\right)^{3}}$$

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

$$\frac{b^{6}\left(c^{5}\right)^{3}}{\left(2a\right)^{3}}$$

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

$$\frac{b^{6}c^{15}}{\left(2a\right)^{3}}$$

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

$$\frac{b^{6}c^{15}}{2^{3}a^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{b^{6}c^{15}}{8a^{3}}$$