Solve [-a^2*(-a^2b)^3]^3

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

Evaluate

$$b^{9}a^{24}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

Expand \left(\left(-a^{2}\right)^{4}b^{3}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(-a^{2}\right)^{12}\left(b^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-a^{2}\right)^{12}b^{9}$$

Expand \left(-a^{2}\right)^{12}.

$$\left(-1\right)^{12}\left(a^{2}\right)^{12}b^{9}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 12 to get 24.

$$\left(-1\right)^{12}a^{24}b^{9}$$

Calculate -1 to the power of 12 and get 1.

$$1a^{24}b^{9}$$

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

$$a^{24}b^{9}$$

Expand

$$b^{9}a^{24}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

Expand \left(\left(-a^{2}\right)^{4}b^{3}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(-a^{2}\right)^{12}\left(b^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-a^{2}\right)^{12}b^{9}$$

Expand \left(-a^{2}\right)^{12}.

$$\left(-1\right)^{12}\left(a^{2}\right)^{12}b^{9}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 12 to get 24.

$$\left(-1\right)^{12}a^{24}b^{9}$$

Calculate -1 to the power of 12 and get 1.

$$1a^{24}b^{9}$$

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

$$a^{24}b^{9}$$