Solve frac{a^{23}b^33}{(a^2b^3)^3}

$$\frac { a ^ { 23 } b ^ { 33 } } { ( a ^ { 2 } b ^ { 3 } ) ^ { 3 } }$$

Evaluate

$$a^{17}b^{24}$$

Solution Steps

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

$$\frac{a^{23}b^{33}}{\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}}$$

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

$$\frac{a^{23}b^{33}}{a^{6}\left(b^{3}\right)^{3}}$$

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

$$\frac{a^{23}b^{33}}{a^{6}b^{9}}$$

Cancel out a^{6}b^{9} in both numerator and denominator.

$$a^{17}b^{24}$$

Expand

$$a^{17}b^{24}$$

Solution Steps

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

$$\frac{a^{23}b^{33}}{\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}}$$

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

$$\frac{a^{23}b^{33}}{a^{6}\left(b^{3}\right)^{3}}$$

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

$$\frac{a^{23}b^{33}}{a^{6}b^{9}}$$

Cancel out a^{6}b^{9} in both numerator and denominator.

$$a^{17}b^{24}$$