Solve (5a/-3b)^-3

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

Evaluate

$$-\frac{27\times \left(\frac{b}{a}\right)^{3}}{125}$$

Solution Steps

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

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

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

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

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{\frac{1}{125}a^{-3}}{\left(-3b\right)^{-3}}$$

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

$$\frac{\frac{1}{125}a^{-3}}{\left(-3\right)^{-3}b^{-3}}$$

Calculate -3 to the power of -3 and get -\frac{1}{27}.

$$\frac{\frac{1}{125}a^{-3}}{-\frac{1}{27}b^{-3}}$$

Expand

$$-\frac{27\times \left(\frac{b}{a}\right)^{3}}{125}$$

Solution Steps

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

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

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

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

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{\frac{1}{125}a^{-3}}{\left(-3b\right)^{-3}}$$

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

$$\frac{\frac{1}{125}a^{-3}}{\left(-3\right)^{-3}b^{-3}}$$

Calculate -3 to the power of -3 and get -\frac{1}{27}.

$$\frac{\frac{1}{125}a^{-3}}{-\frac{1}{27}b^{-3}}$$