Solve (a^-2/b^-2)^1(b/a)^3=

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

Evaluate

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

Solution Steps

Calculate \frac{a^{-2}}{b^{-2}} to the power of 1 and get \frac{a^{-2}}{b^{-2}}.

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

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

$$\frac{a^{-2}}{b^{-2}}\times \frac{b^{3}}{a^{3}}$$

Multiply \frac{a^{-2}}{b^{-2}} times \frac{b^{3}}{a^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a^{-2}b^{3}}{b^{-2}a^{3}}$$

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

$$\frac{a^{-2}b^{5}}{a^{3}}$$

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

$$\frac{b^{5}}{a^{5}}$$

Expand

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

Solution Steps

Calculate \frac{a^{-2}}{b^{-2}} to the power of 1 and get \frac{a^{-2}}{b^{-2}}.

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

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

$$\frac{a^{-2}}{b^{-2}}\times \frac{b^{3}}{a^{3}}$$

Multiply \frac{a^{-2}}{b^{-2}} times \frac{b^{3}}{a^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a^{-2}b^{3}}{b^{-2}a^{3}}$$

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

$$\frac{a^{-2}b^{5}}{a^{3}}$$

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

$$\frac{b^{5}}{a^{5}}$$