Solve (frac{a^{-2}b^5c^-4}{ac^-1})^5

$$( \frac { a ^ { - 2 } b ^ { 5 } c ^ { - 4 } } { a c ^ { - 1 } } ) ^ { 5 }$$

Evaluate

$$\frac{b^{25}}{\left(ac\right)^{15}}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{b^{25}}{\left(a^{3}c^{3}\right)^{5}}$$

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

$$\frac{b^{25}}{\left(a^{3}\right)^{5}\left(c^{3}\right)^{5}}$$

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

$$\frac{b^{25}}{a^{15}\left(c^{3}\right)^{5}}$$

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

$$\frac{b^{25}}{a^{15}c^{15}}$$

Expand

$$\frac{b^{25}}{\left(ac\right)^{15}}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{b^{25}}{\left(a^{3}c^{3}\right)^{5}}$$

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

$$\frac{b^{25}}{\left(a^{3}\right)^{5}\left(c^{3}\right)^{5}}$$

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

$$\frac{b^{25}}{a^{15}\left(c^{3}\right)^{5}}$$

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

$$\frac{b^{25}}{a^{15}c^{15}}$$