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

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

Evaluate

$$a^{14}b^{18}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\left(-a^{2}\right)^{6}b^{18}a^{2}$$

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

$$\left(-1\right)^{6}\left(a^{2}\right)^{6}b^{18}a^{2}$$

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

$$\left(-1\right)^{6}a^{12}b^{18}a^{2}$$

Calculate -1 to the power of 6 and get 1.

$$1a^{12}b^{18}a^{2}$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$1a^{14}b^{18}$$

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

$$a^{14}b^{18}$$

Expand

$$a^{14}b^{18}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\left(-a^{2}\right)^{6}b^{18}a^{2}$$

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

$$\left(-1\right)^{6}\left(a^{2}\right)^{6}b^{18}a^{2}$$

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

$$\left(-1\right)^{6}a^{12}b^{18}a^{2}$$

Calculate -1 to the power of 6 and get 1.

$$1a^{12}b^{18}a^{2}$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$1a^{14}b^{18}$$

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

$$a^{14}b^{18}$$