Solve [a^{3}*(-a^{4})]^{3}div(a^2)^3*(a^2)^3

$$[ a ^ { 3 } \cdot ( - a ^ { 4 } ) ] ^ { 3 } \div ( a ^ { 2 } ) ^ { 3 } \cdot ( a ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-a^{21}$$

Solution Steps

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

$$\frac{\left(a^{3}\left(-a^{4}\right)\right)^{3}}{a^{6}}\left(a^{2}\right)^{3}$$

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

$$\frac{\left(a^{3}\left(-a^{4}\right)\right)^{3}}{a^{6}}a^{6}$$

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

$$\frac{\left(a^{3}\right)^{3}\left(-a^{4}\right)^{3}}{a^{6}}a^{6}$$

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

$$\frac{a^{9}\left(-a^{4}\right)^{3}}{a^{6}}a^{6}$$

Cancel out a^{6} in both numerator and denominator.

$$a^{3}\left(-a^{4}\right)^{3}a^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$a^{9}\left(-a^{4}\right)^{3}$$

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

$$a^{9}\left(-1\right)^{3}\left(a^{4}\right)^{3}$$

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

$$a^{9}\left(-1\right)^{3}a^{12}$$

Calculate -1 to the power of 3 and get -1.

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

To multiply powers of the same base, add their exponents. Add 9 and 12 to get 21.

$$a^{21}\left(-1\right)$$

Expand

$$-a^{21}$$

Solution Steps

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

$$\frac{\left(a^{3}\left(-a^{4}\right)\right)^{3}}{a^{6}}\left(a^{2}\right)^{3}$$

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

$$\frac{\left(a^{3}\left(-a^{4}\right)\right)^{3}}{a^{6}}a^{6}$$

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

$$\frac{\left(a^{3}\right)^{3}\left(-a^{4}\right)^{3}}{a^{6}}a^{6}$$

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

$$\frac{a^{9}\left(-a^{4}\right)^{3}}{a^{6}}a^{6}$$

Cancel out a^{6} in both numerator and denominator.

$$a^{3}\left(-a^{4}\right)^{3}a^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$a^{9}\left(-a^{4}\right)^{3}$$

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

$$a^{9}\left(-1\right)^{3}\left(a^{4}\right)^{3}$$

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

$$a^{9}\left(-1\right)^{3}a^{12}$$

Calculate -1 to the power of 3 and get -1.

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

To multiply powers of the same base, add their exponents. Add 9 and 12 to get 21.

$$a^{21}\left(-1\right)$$