Solve frac{a^{-5}b^2}{(a^-1b^-3)^2}

$$\frac { a ^ { - 5 } b ^ { 2 } } { ( a ^ { - 1 } b ^ { - 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{b^{8}}{a^{3}}$$

Solution Steps

Expand \left(a^{-1}b^{-3}\right)^{2}.

$$\frac{a^{-5}b^{2}}{\left(a^{-1}\right)^{2}\left(b^{-3}\right)^{2}}$$

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

$$\frac{a^{-5}b^{2}}{a^{-2}\left(b^{-3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$\frac{a^{-5}b^{2}}{a^{-2}b^{-6}}$$

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

$$\frac{a^{-5}b^{8}}{a^{-2}}$$

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

$$\frac{b^{8}}{a^{3}}$$

Expand

$$\frac{b^{8}}{a^{3}}$$

Solution Steps

Expand \left(a^{-1}b^{-3}\right)^{2}.

$$\frac{a^{-5}b^{2}}{\left(a^{-1}\right)^{2}\left(b^{-3}\right)^{2}}$$

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

$$\frac{a^{-5}b^{2}}{a^{-2}\left(b^{-3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$\frac{a^{-5}b^{2}}{a^{-2}b^{-6}}$$

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

$$\frac{a^{-5}b^{8}}{a^{-2}}$$

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

$$\frac{b^{8}}{a^{3}}$$