Solve y^{18}divy^{12}-y^2*y^4+(-2y^2)^3

$$y ^ { 18 } \div y ^ { 12 } - y ^ { 2 } \cdot y ^ { 4 } + ( - 2 y ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-8y^{6}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 18 to get 6.

$$y^{6}-y^{2}y^{4}+\left(-2y^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

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

Combine y^{6} and -y^{6} to get 0.

$$0+\left(-2y^{2}\right)^{3}$$

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

$$0+\left(-2\right)^{3}\left(y^{2}\right)^{3}$$

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

$$0+\left(-2\right)^{3}y^{6}$$

Calculate -2 to the power of 3 and get -8.

$$0-8y^{6}$$

Anything plus zero gives itself.

$$-8y^{6}$$

Expand

$$-8y^{6}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 18 to get 6.

$$y^{6}-y^{2}y^{4}+\left(-2y^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

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

Combine y^{6} and -y^{6} to get 0.

$$0+\left(-2y^{2}\right)^{3}$$

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

$$0+\left(-2\right)^{3}\left(y^{2}\right)^{3}$$

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

$$0+\left(-2\right)^{3}y^{6}$$

Calculate -2 to the power of 3 and get -8.

$$0-8y^{6}$$

Anything plus zero gives itself.

$$-8y^{6}$$