Solve frac{(-4a^{-7}y^5)^3}{8a^-10y^-7}

$$\frac { ( - 4 a ^ { - 7 } y ^ { 5 } ) ^ { 3 } } { 8 a ^ { - 10 } y ^ { - 7 } }$$

Evaluate

$$-\frac{8y^{22}}{a^{11}}$$

Solution Steps

Expand \left(-4a^{-7}y^{5}\right)^{3}.

$$\frac{\left(-4\right)^{3}\left(a^{-7}\right)^{3}\left(y^{5}\right)^{3}}{8a^{-10}y^{-7}}$$

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

$$\frac{\left(-4\right)^{3}a^{-21}\left(y^{5}\right)^{3}}{8a^{-10}y^{-7}}$$

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

$$\frac{\left(-4\right)^{3}a^{-21}y^{15}}{8a^{-10}y^{-7}}$$

Calculate -4 to the power of 3 and get -64.

$$\frac{-64a^{-21}y^{15}}{8a^{-10}y^{-7}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{-8a^{-21}y^{15}}{a^{-10}y^{-7}}$$

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

$$\frac{-8a^{-21}y^{22}}{a^{-10}}$$

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

$$\frac{-8y^{22}}{a^{11}}$$

Expand

$$-\frac{8y^{22}}{a^{11}}$$

Solution Steps

Expand \left(-4a^{-7}y^{5}\right)^{3}.

$$\frac{\left(-4\right)^{3}\left(a^{-7}\right)^{3}\left(y^{5}\right)^{3}}{8a^{-10}y^{-7}}$$

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

$$\frac{\left(-4\right)^{3}a^{-21}\left(y^{5}\right)^{3}}{8a^{-10}y^{-7}}$$

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

$$\frac{\left(-4\right)^{3}a^{-21}y^{15}}{8a^{-10}y^{-7}}$$

Calculate -4 to the power of 3 and get -64.

$$\frac{-64a^{-21}y^{15}}{8a^{-10}y^{-7}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{-8a^{-21}y^{15}}{a^{-10}y^{-7}}$$

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

$$\frac{-8a^{-21}y^{22}}{a^{-10}}$$

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

$$\frac{-8y^{22}}{a^{11}}$$