Solve (6)a^{2}*a^{3}-(-a^{2})^{3}-2a*(a^{2})^3-2[(a^3)^3diva^3]

$$( 6 ) a ^ { 2 } \cdot a ^ { 3 } - ( - a ^ { 2 } ) ^ { 3 } - 2 a \cdot ( a ^ { 2 } ) ^ { 3 } - 2 [ ( a ^ { 3 } ) ^ { 3 } \div a ^ { 3 } ]$$

Evaluate

$$-\left(2a-3\right)\left(a+2\right)a^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$6a^{5}-\left(-a^{2}\right)^{3}-2a\left(a^{2}\right)^{3}-2\times \frac{\left(a^{3}\right)^{3}}{a^{3}}$$

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

$$6a^{5}-\left(-a^{2}\right)^{3}-2aa^{6}-2\times \frac{\left(a^{3}\right)^{3}}{a^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$6a^{5}-\left(-a^{2}\right)^{3}-2a^{7}-2\times \frac{\left(a^{3}\right)^{3}}{a^{3}}$$

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

$$6a^{5}-\left(-a^{2}\right)^{3}-2a^{7}-2\times \frac{a^{9}}{a^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 9 to get 6.

$$6a^{5}-\left(-a^{2}\right)^{3}-2a^{7}-2a^{6}$$

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

$$6a^{5}-\left(-1\right)^{3}\left(a^{2}\right)^{3}-2a^{7}-2a^{6}$$

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

$$6a^{5}-\left(-1\right)^{3}a^{6}-2a^{7}-2a^{6}$$

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

$$6a^{5}-\left(-a^{6}\right)-2a^{7}-2a^{6}$$

Multiply -1 and -1 to get 1.

$$6a^{5}+a^{6}-2a^{7}-2a^{6}$$

Combine a^{6} and -2a^{6} to get -a^{6}.

$$6a^{5}-a^{6}-2a^{7}$$

Expand

$$6a^{5}-a^{6}-2a^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$6a^{5}-\left(-a^{2}\right)^{3}-2a\left(a^{2}\right)^{3}-2\times \frac{\left(a^{3}\right)^{3}}{a^{3}}$$

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

$$6a^{5}-\left(-a^{2}\right)^{3}-2aa^{6}-2\times \frac{\left(a^{3}\right)^{3}}{a^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$6a^{5}-\left(-a^{2}\right)^{3}-2a^{7}-2\times \frac{\left(a^{3}\right)^{3}}{a^{3}}$$

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

$$6a^{5}-\left(-a^{2}\right)^{3}-2a^{7}-2\times \frac{a^{9}}{a^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 9 to get 6.

$$6a^{5}-\left(-a^{2}\right)^{3}-2a^{7}-2a^{6}$$

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

$$6a^{5}-\left(-1\right)^{3}\left(a^{2}\right)^{3}-2a^{7}-2a^{6}$$

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

$$6a^{5}-\left(-1\right)^{3}a^{6}-2a^{7}-2a^{6}$$

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

$$6a^{5}-\left(-a^{6}\right)-2a^{7}-2a^{6}$$

Multiply -1 and -1 to get 1.

$$6a^{5}+a^{6}-2a^{7}-2a^{6}$$

Combine a^{6} and -2a^{6} to get -a^{6}.

$$6a^{5}-a^{6}-2a^{7}$$