Solve 5a^3b*(3b)^2-(-6ab)^2*(-ab)

$$5 a ^ { 3 } b \cdot ( 3 b ) ^ { 2 } - ( - 6 a b ) ^ { 2 } \cdot ( - a b )$$

Evaluate

$$81\left(ab\right)^{3}$$

Solution Steps

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

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

Calculate 3 to the power of 2 and get 9.

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

Multiply 5 and 9 to get 45.

$$45a^{3}bb^{2}-\left(-6ab\right)^{2}\left(-a\right)b$$

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

$$45a^{3}b^{3}-\left(-6ab\right)^{2}\left(-a\right)b$$

Expand \left(-6ab\right)^{2}.

$$45a^{3}b^{3}-\left(-6\right)^{2}a^{2}b^{2}\left(-a\right)b$$

Calculate -6 to the power of 2 and get 36.

$$45a^{3}b^{3}-36a^{2}b^{2}\left(-a\right)b$$

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

$$45a^{3}b^{3}-36a^{2}b^{3}\left(-a\right)$$

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

$$45a^{3}b^{3}-36a^{3}b^{3}\left(-1\right)$$

Multiply -36 and -1 to get 36.

$$45a^{3}b^{3}+36a^{3}b^{3}$$

Combine 45a^{3}b^{3} and 36a^{3}b^{3} to get 81a^{3}b^{3}.

$$81a^{3}b^{3}$$

Expand

$$81\left(ab\right)^{3}$$

Solution Steps

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

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

Calculate 3 to the power of 2 and get 9.

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

Multiply 5 and 9 to get 45.

$$45a^{3}bb^{2}-\left(-6ab\right)^{2}\left(-a\right)b$$

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

$$45a^{3}b^{3}-\left(-6ab\right)^{2}\left(-a\right)b$$

Expand \left(-6ab\right)^{2}.

$$45a^{3}b^{3}-\left(-6\right)^{2}a^{2}b^{2}\left(-a\right)b$$

Calculate -6 to the power of 2 and get 36.

$$45a^{3}b^{3}-36a^{2}b^{2}\left(-a\right)b$$

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

$$45a^{3}b^{3}-36a^{2}b^{3}\left(-a\right)$$

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

$$45a^{3}b^{3}-36a^{3}b^{3}\left(-1\right)$$

Multiply -36 and -1 to get 36.

$$45a^{3}b^{3}+36a^{3}b^{3}$$

Combine 45a^{3}b^{3} and 36a^{3}b^{3} to get 81a^{3}b^{3}.

$$81a^{3}b^{3}$$