Solve a^{3}*(-b^{3})^2+(-2ab^2)^4div(-2ab^2)

$$a ^ { 3 } \cdot ( - b ^ { 3 } ) ^ { 2 } + ( - 2 a b ^ { 2 } ) ^ { 4 } \div ( - 2 a b ^ { 2 } )$$

Evaluate

$$-7a^{3}b^{6}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 4 to get 3.

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

Calculate -b^{3} to the power of 2 and get \left(b^{3}\right)^{2}.

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

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

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

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

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

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

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

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

$$a^{3}b^{6}-8a^{3}b^{6}$$

Combine a^{3}b^{6} and -8a^{3}b^{6} to get -7a^{3}b^{6}.

$$-7a^{3}b^{6}$$

Expand

$$-7a^{3}b^{6}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 4 to get 3.

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

Calculate -b^{3} to the power of 2 and get \left(b^{3}\right)^{2}.

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

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

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

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

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

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

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

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

$$a^{3}b^{6}-8a^{3}b^{6}$$

Combine a^{3}b^{6} and -8a^{3}b^{6} to get -7a^{3}b^{6}.

$$-7a^{3}b^{6}$$