Solve (a^{7}*b^{8})^3:(a^3*b^5)^2=

$$( a ^ { 7 } \cdot b ^ { 8 } ) ^ { 3 } : ( a ^ { 3 } \cdot b ^ { 5 } ) ^ { 2 } =$$

Evaluate

$$b^{14}a^{15}$$

Solution Steps

Expand \left(a^{7}b^{8}\right)^{3}.

$$\frac{\left(a^{7}\right)^{3}\left(b^{8}\right)^{3}}{\left(a^{3}b^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{a^{21}\left(b^{8}\right)^{3}}{\left(a^{3}b^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{a^{21}b^{24}}{\left(a^{3}b^{5}\right)^{2}}$$

Expand \left(a^{3}b^{5}\right)^{2}.

$$\frac{a^{21}b^{24}}{\left(a^{3}\right)^{2}\left(b^{5}\right)^{2}}$$

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

$$\frac{a^{21}b^{24}}{a^{6}\left(b^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{a^{21}b^{24}}{a^{6}b^{10}}$$

Cancel out a^{6}b^{10} in both numerator and denominator.

$$b^{14}a^{15}$$

Expand

$$b^{14}a^{15}$$

Solution Steps

Expand \left(a^{7}b^{8}\right)^{3}.

$$\frac{\left(a^{7}\right)^{3}\left(b^{8}\right)^{3}}{\left(a^{3}b^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{a^{21}\left(b^{8}\right)^{3}}{\left(a^{3}b^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{a^{21}b^{24}}{\left(a^{3}b^{5}\right)^{2}}$$

Expand \left(a^{3}b^{5}\right)^{2}.

$$\frac{a^{21}b^{24}}{\left(a^{3}\right)^{2}\left(b^{5}\right)^{2}}$$

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

$$\frac{a^{21}b^{24}}{a^{6}\left(b^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{a^{21}b^{24}}{a^{6}b^{10}}$$

Cancel out a^{6}b^{10} in both numerator and denominator.

$$b^{14}a^{15}$$