Solve (3a^2)^3:(-1/3a)^5

$$( 3 a ^ { 2 } ) ^ { 3 } : ( - \frac { 1 } { 3 } a ) ^ { 5 }$$

Evaluate

$$-6561a$$

Solution Steps

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

$$\frac{3^{3}\left(a^{2}\right)^{3}}{\left(-\frac{1}{3}a\right)^{5}}$$

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

$$\frac{3^{3}a^{6}}{\left(-\frac{1}{3}a\right)^{5}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27a^{6}}{\left(-\frac{1}{3}a\right)^{5}}$$

Expand \left(-\frac{1}{3}a\right)^{5}.

$$\frac{27a^{6}}{\left(-\frac{1}{3}\right)^{5}a^{5}}$$

Calculate -\frac{1}{3} to the power of 5 and get -\frac{1}{243}.

$$\frac{27a^{6}}{-\frac{1}{243}a^{5}}$$

Cancel out a^{5} in both numerator and denominator.

$$\frac{27a}{-\frac{1}{243}}$$

Divide 27a by -\frac{1}{243} by multiplying 27a by the reciprocal of -\frac{1}{243}.

$$\frac{27a\times 243}{-1}$$

Multiply 27 and 243 to get 6561.

$$\frac{6561a}{-1}$$

Anything divided by -1 gives its opposite.

$$-6561a$$

Expand

$$-6561a$$

Solution Steps

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

$$\frac{3^{3}\left(a^{2}\right)^{3}}{\left(-\frac{1}{3}a\right)^{5}}$$

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

$$\frac{3^{3}a^{6}}{\left(-\frac{1}{3}a\right)^{5}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27a^{6}}{\left(-\frac{1}{3}a\right)^{5}}$$

Expand \left(-\frac{1}{3}a\right)^{5}.

$$\frac{27a^{6}}{\left(-\frac{1}{3}\right)^{5}a^{5}}$$

Calculate -\frac{1}{3} to the power of 5 and get -\frac{1}{243}.

$$\frac{27a^{6}}{-\frac{1}{243}a^{5}}$$

Cancel out a^{5} in both numerator and denominator.

$$\frac{27a}{-\frac{1}{243}}$$

Divide 27a by -\frac{1}{243} by multiplying 27a by the reciprocal of -\frac{1}{243}.

$$\frac{27a\times 243}{-1}$$

Multiply 27 and 243 to get 6561.

$$\frac{6561a}{-1}$$

Anything divided by -1 gives its opposite.

$$-6561a$$