Solve (-3a^{2}b)^{3}-60a^{7}b^3:(-20a)+6a^5*(-12ab^3+9ab^3)]:(-21

$$( - 3 a ^ { 2 } b ) ^ { 3 } - 60 a ^ { 7 } b ^ { 3 } : ( - 20 a ) + 6 a ^ { 5 } \cdot ( - 12 a b ^ { 3 } + 9 a b ^ { 3 } ) ] : ( - 21$$

Evaluate

$$-42b^{3}a^{6}$$

Solution Steps

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

$$\left(-3\right)^{3}\left(a^{2}\right)^{3}b^{3}-\frac{60a^{7}b^{3}}{-20a}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

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

$$\left(-3\right)^{3}a^{6}b^{3}-\frac{60a^{7}b^{3}}{-20a}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

Calculate -3 to the power of 3 and get -27.

$$-27a^{6}b^{3}-\frac{60a^{7}b^{3}}{-20a}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

Cancel out 20a in both numerator and denominator.

$$-27a^{6}b^{3}-\frac{3b^{3}a^{6}}{-1}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

Anything divided by -1 gives its opposite.

$$-27a^{6}b^{3}-\left(-3b^{3}a^{6}\right)+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

The opposite of -3b^{3}a^{6} is 3b^{3}a^{6}.

$$-27a^{6}b^{3}+3b^{3}a^{6}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

Combine -27a^{6}b^{3} and 3b^{3}a^{6} to get -24a^{6}b^{3}.

$$-24a^{6}b^{3}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

Combine -12ab^{3} and 9ab^{3} to get -3ab^{3}.

$$-24a^{6}b^{3}+6a^{5}\left(-3\right)ab^{3}$$

Multiply 6 and -3 to get -18.

$$-24a^{6}b^{3}-18a^{5}ab^{3}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$-24a^{6}b^{3}-18a^{6}b^{3}$$

Combine -24a^{6}b^{3} and -18a^{6}b^{3} to get -42a^{6}b^{3}.

$$-42a^{6}b^{3}$$

Expand

$$-42b^{3}a^{6}$$

Solution Steps

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

$$\left(-3\right)^{3}\left(a^{2}\right)^{3}b^{3}-\frac{60a^{7}b^{3}}{-20a}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

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

$$\left(-3\right)^{3}a^{6}b^{3}-\frac{60a^{7}b^{3}}{-20a}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

Calculate -3 to the power of 3 and get -27.

$$-27a^{6}b^{3}-\frac{60a^{7}b^{3}}{-20a}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

Cancel out 20a in both numerator and denominator.

$$-27a^{6}b^{3}-\frac{3b^{3}a^{6}}{-1}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

Anything divided by -1 gives its opposite.

$$-27a^{6}b^{3}-\left(-3b^{3}a^{6}\right)+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

The opposite of -3b^{3}a^{6} is 3b^{3}a^{6}.

$$-27a^{6}b^{3}+3b^{3}a^{6}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

Combine -27a^{6}b^{3} and 3b^{3}a^{6} to get -24a^{6}b^{3}.

$$-24a^{6}b^{3}+6a^{5}\left(-12ab^{3}+9ab^{3}\right)$$

Combine -12ab^{3} and 9ab^{3} to get -3ab^{3}.

$$-24a^{6}b^{3}+6a^{5}\left(-3\right)ab^{3}$$

Multiply 6 and -3 to get -18.

$$-24a^{6}b^{3}-18a^{5}ab^{3}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$-24a^{6}b^{3}-18a^{6}b^{3}$$

Combine -24a^{6}b^{3} and -18a^{6}b^{3} to get -42a^{6}b^{3}.

$$-42a^{6}b^{3}$$