Solve a*a^{2}*a^{3}+(-2a^3)^2-a^8diva^2

$$a \cdot a ^ { 2 } \cdot a ^ { 3 } + ( - 2 a ^ { 3 } ) ^ { 2 } - a ^ { 8 } \div a ^ { 2 }$$

Evaluate

$$4a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$a^{3}a^{3}+\left(-2a^{3}\right)^{2}-\frac{a^{8}}{a^{2}}$$

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

$$a^{6}+\left(-2a^{3}\right)^{2}-\frac{a^{8}}{a^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 8 to get 6.

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

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

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

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

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

Calculate -2 to the power of 2 and get 4.

$$a^{6}+4a^{6}-a^{6}$$

Combine a^{6} and 4a^{6} to get 5a^{6}.

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

Combine 5a^{6} and -a^{6} to get 4a^{6}.

$$4a^{6}$$

Expand

$$4a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$a^{3}a^{3}+\left(-2a^{3}\right)^{2}-\frac{a^{8}}{a^{2}}$$

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

$$a^{6}+\left(-2a^{3}\right)^{2}-\frac{a^{8}}{a^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 8 to get 6.

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

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

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

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

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

Calculate -2 to the power of 2 and get 4.

$$a^{6}+4a^{6}-a^{6}$$

Combine a^{6} and 4a^{6} to get 5a^{6}.

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

Combine 5a^{6} and -a^{6} to get 4a^{6}.

$$4a^{6}$$