Solve (b^{2})^{3}*(-b^3)^4div(b^5)^3

$$( b ^ { 2 } ) ^ { 3 } \cdot ( - b ^ { 3 } ) ^ { 4 } \div ( b ^ { 5 } ) ^ { 3 }$$

Evaluate

$$b^{3}$$

Solution Steps

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

$$\frac{b^{6}\left(-b^{3}\right)^{4}}{\left(b^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{b^{6}\left(-b^{3}\right)^{4}}{b^{15}}$$

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

$$\frac{\left(-b^{3}\right)^{4}}{b^{9}}$$

Expand \left(-b^{3}\right)^{4}.

$$\frac{\left(-1\right)^{4}\left(b^{3}\right)^{4}}{b^{9}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\left(-1\right)^{4}b^{12}}{b^{9}}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{1b^{12}}{b^{9}}$$

Cancel out b^{9} in both numerator and denominator.

$$b^{3}$$

Expand

$$b^{3}$$

Solution Steps

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

$$\frac{b^{6}\left(-b^{3}\right)^{4}}{\left(b^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{b^{6}\left(-b^{3}\right)^{4}}{b^{15}}$$

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

$$\frac{\left(-b^{3}\right)^{4}}{b^{9}}$$

Expand \left(-b^{3}\right)^{4}.

$$\frac{\left(-1\right)^{4}\left(b^{3}\right)^{4}}{b^{9}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\left(-1\right)^{4}b^{12}}{b^{9}}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{1b^{12}}{b^{9}}$$

Cancel out b^{9} in both numerator and denominator.

$$b^{3}$$