Solve -54q(-7a^2)^-1/(3a^-4)^3

$$- 54 q \frac { ( - 7 a ^ { 2 } ) ^ { - 1 } } { ( 3 a ^ { - 4 } ) ^ { 3 } }$$

Evaluate

$$\frac{2qa^{10}}{7}$$

Solution Steps

Expand \left(-7a^{2}\right)^{-1}.

$$-54q\times \frac{\left(-7\right)^{-1}\left(a^{2}\right)^{-1}}{\left(3a^{-4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$-54q\times \frac{\left(-7\right)^{-1}a^{-2}}{\left(3a^{-4}\right)^{3}}$$

Calculate -7 to the power of -1 and get -\frac{1}{7}.

$$-54q\times \frac{-\frac{1}{7}a^{-2}}{\left(3a^{-4}\right)^{3}}$$

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

$$-54q\times \frac{-\frac{1}{7}a^{-2}}{3^{3}\left(a^{-4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 3 to get -12.

$$-54q\times \frac{-\frac{1}{7}a^{-2}}{3^{3}a^{-12}}$$

Calculate 3 to the power of 3 and get 27.

$$-54q\times \frac{-\frac{1}{7}a^{-2}}{27a^{-12}}$$

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

$$-54q\times \frac{-\frac{1}{7}a^{10}}{27}$$

Divide -\frac{1}{7}a^{10} by 27 to get -\frac{1}{189}a^{10}.

$$-54q\left(-\frac{1}{189}\right)a^{10}$$

Multiply -54 and -\frac{1}{189} to get \frac{2}{7}.

$$\frac{2}{7}qa^{10}$$

Expand

$$\frac{2qa^{10}}{7}$$

Solution Steps

Expand \left(-7a^{2}\right)^{-1}.

$$-54q\times \frac{\left(-7\right)^{-1}\left(a^{2}\right)^{-1}}{\left(3a^{-4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$-54q\times \frac{\left(-7\right)^{-1}a^{-2}}{\left(3a^{-4}\right)^{3}}$$

Calculate -7 to the power of -1 and get -\frac{1}{7}.

$$-54q\times \frac{-\frac{1}{7}a^{-2}}{\left(3a^{-4}\right)^{3}}$$

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

$$-54q\times \frac{-\frac{1}{7}a^{-2}}{3^{3}\left(a^{-4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 3 to get -12.

$$-54q\times \frac{-\frac{1}{7}a^{-2}}{3^{3}a^{-12}}$$

Calculate 3 to the power of 3 and get 27.

$$-54q\times \frac{-\frac{1}{7}a^{-2}}{27a^{-12}}$$

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

$$-54q\times \frac{-\frac{1}{7}a^{10}}{27}$$

Divide -\frac{1}{7}a^{10} by 27 to get -\frac{1}{189}a^{10}.

$$-54q\left(-\frac{1}{189}\right)a^{10}$$

Multiply -54 and -\frac{1}{189} to get \frac{2}{7}.

$$\frac{2}{7}qa^{10}$$