Solve (x*x^2)^3div(-1/3x^3)^2

$$( x \cdot x ^ { 2 } ) ^ { 3 } \div ( - \frac { 1 } { 3 } x ^ { 3 } ) ^ { 2 }$$

Evaluate

$$9x^{3}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{x^{9}}{\left(-\frac{1}{3}x^{3}\right)^{2}}$$

Expand \left(-\frac{1}{3}x^{3}\right)^{2}.

$$\frac{x^{9}}{\left(-\frac{1}{3}\right)^{2}\left(x^{3}\right)^{2}}$$

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

$$\frac{x^{9}}{\left(-\frac{1}{3}\right)^{2}x^{6}}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{x^{9}}{\frac{1}{9}x^{6}}$$

Cancel out x^{6} in both numerator and denominator.

$$\frac{x^{3}}{\frac{1}{9}}$$

Divide x^{3} by \frac{1}{9} by multiplying x^{3} by the reciprocal of \frac{1}{9}.

$$x^{3}\times 9$$

Expand

$$9x^{3}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{x^{9}}{\left(-\frac{1}{3}x^{3}\right)^{2}}$$

Expand \left(-\frac{1}{3}x^{3}\right)^{2}.

$$\frac{x^{9}}{\left(-\frac{1}{3}\right)^{2}\left(x^{3}\right)^{2}}$$

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

$$\frac{x^{9}}{\left(-\frac{1}{3}\right)^{2}x^{6}}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{x^{9}}{\frac{1}{9}x^{6}}$$

Cancel out x^{6} in both numerator and denominator.

$$\frac{x^{3}}{\frac{1}{9}}$$

Divide x^{3} by \frac{1}{9} by multiplying x^{3} by the reciprocal of \frac{1}{9}.

$$x^{3}\times 9$$