Solve [-(ab^2)^3]^-2

$$[ - ( a b ^ { 2 } ) ^ { 3 } ] ^ { - 2 }$$

Evaluate

$$\frac{1}{a^{6}b^{12}}$$

Solution Steps

Expand \left(ab^{2}\right)^{3}.

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

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

$$\left(-a^{3}b^{6}\right)^{-2}$$

Expand \left(-a^{3}b^{6}\right)^{-2}.

$$\left(-1\right)^{-2}\left(a^{3}\right)^{-2}\left(b^{6}\right)^{-2}$$

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

$$\left(-1\right)^{-2}a^{-6}\left(b^{6}\right)^{-2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\left(-1\right)^{-2}a^{-6}b^{-12}$$

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

$$1a^{-6}b^{-12}$$

For any term t, t\times 1=t and 1t=t.

$$a^{-6}b^{-12}$$

Expand

$$\frac{1}{a^{6}b^{12}}$$

Solution Steps

Expand \left(ab^{2}\right)^{3}.

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

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

$$\left(-a^{3}b^{6}\right)^{-2}$$

Expand \left(-a^{3}b^{6}\right)^{-2}.

$$\left(-1\right)^{-2}\left(a^{3}\right)^{-2}\left(b^{6}\right)^{-2}$$

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

$$\left(-1\right)^{-2}a^{-6}\left(b^{6}\right)^{-2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\left(-1\right)^{-2}a^{-6}b^{-12}$$

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

$$1a^{-6}b^{-12}$$

For any term t, t\times 1=t and 1t=t.

$$a^{-6}b^{-12}$$