Solve (a^3b)^-1/(-ab^-4)^-2

$$\frac { ( a ^ { 3 } b ) ^ { - 1 } } { ( - a b ^ { - 4 } ) ^ { - 2 } }$$

Evaluate

$$\frac{1}{ab^{9}}$$

Short Solution Steps

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

$$\frac{\left(a^{3}\right)^{-1}b^{-1}}{\left(\left(-a\right)b^{-4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$\frac{a^{-3}b^{-1}}{\left(\left(-a\right)b^{-4}\right)^{-2}}$$

Expand \left(\left(-a\right)b^{-4}\right)^{-2}.

$$\frac{a^{-3}b^{-1}}{\left(-a\right)^{-2}\left(b^{-4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -2 to get 8.

$$\frac{a^{-3}b^{-1}}{\left(-a\right)^{-2}b^{8}}$$

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

$$\frac{a^{-3}}{\left(-a\right)^{-2}b^{9}}$$

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

$$\frac{a^{-3}}{\left(-1\right)^{-2}a^{-2}b^{9}}$$

Calculate -1 to the power of -2 and get 1.

$$\frac{a^{-3}}{1a^{-2}b^{9}}$$

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

$$\frac{1}{a^{1}b^{9}}$$

Calculate a to the power of 1 and get a.

$$\frac{1}{ab^{9}}$$

Expand

$$\frac{1}{ab^{9}}$$

Short Solution Steps

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

$$\frac{\left(a^{3}\right)^{-1}b^{-1}}{\left(\left(-a\right)b^{-4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$\frac{a^{-3}b^{-1}}{\left(\left(-a\right)b^{-4}\right)^{-2}}$$

Expand \left(\left(-a\right)b^{-4}\right)^{-2}.

$$\frac{a^{-3}b^{-1}}{\left(-a\right)^{-2}\left(b^{-4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -2 to get 8.

$$\frac{a^{-3}b^{-1}}{\left(-a\right)^{-2}b^{8}}$$

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

$$\frac{a^{-3}}{\left(-a\right)^{-2}b^{9}}$$

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

$$\frac{a^{-3}}{\left(-1\right)^{-2}a^{-2}b^{9}}$$

Calculate -1 to the power of -2 and get 1.

$$\frac{a^{-3}}{1a^{-2}b^{9}}$$

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

$$\frac{1}{a^{1}b^{9}}$$

Calculate a to the power of 1 and get a.

$$\frac{1}{ab^{9}}$$