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

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

Evaluate

$$6561a^{13}b^{29}$$

Solution Steps

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

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

Expand \left(3a^{2}b^{7}\right)^{3}.

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

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

$$\frac{3^{3}a^{6}\left(b^{7}\right)^{3}}{a^{3}b^{2}}\times \left(3a^{2}b^{2}\right)^{5}$$

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

$$\frac{3^{3}a^{6}b^{21}}{a^{3}b^{2}}\times \left(3a^{2}b^{2}\right)^{5}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27a^{6}b^{21}}{a^{3}b^{2}}\times \left(3a^{2}b^{2}\right)^{5}$$

Cancel out b^{2}a^{3} in both numerator and denominator.

$$27a^{3}b^{19}\times \left(3a^{2}b^{2}\right)^{5}$$

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

$$27a^{3}b^{19}\times 3^{5}\left(a^{2}\right)^{5}\left(b^{2}\right)^{5}$$

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

$$27a^{3}b^{19}\times 3^{5}a^{10}\left(b^{2}\right)^{5}$$

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

$$27a^{3}b^{19}\times 3^{5}a^{10}b^{10}$$

Calculate 3 to the power of 5 and get 243.

$$27a^{3}b^{19}\times 243a^{10}b^{10}$$

Multiply 27 and 243 to get 6561.

$$6561a^{3}b^{19}a^{10}b^{10}$$

To multiply powers of the same base, add their exponents. Add 3 and 10 to get 13.

$$6561a^{13}b^{19}b^{10}$$

To multiply powers of the same base, add their exponents. Add 19 and 10 to get 29.

$$6561a^{13}b^{29}$$

Expand

$$6561a^{13}b^{29}$$

Solution Steps

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

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

Expand \left(3a^{2}b^{7}\right)^{3}.

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

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

$$\frac{3^{3}a^{6}\left(b^{7}\right)^{3}}{a^{3}b^{2}}\times \left(3a^{2}b^{2}\right)^{5}$$

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

$$\frac{3^{3}a^{6}b^{21}}{a^{3}b^{2}}\times \left(3a^{2}b^{2}\right)^{5}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27a^{6}b^{21}}{a^{3}b^{2}}\times \left(3a^{2}b^{2}\right)^{5}$$

Cancel out b^{2}a^{3} in both numerator and denominator.

$$27a^{3}b^{19}\times \left(3a^{2}b^{2}\right)^{5}$$

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

$$27a^{3}b^{19}\times 3^{5}\left(a^{2}\right)^{5}\left(b^{2}\right)^{5}$$

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

$$27a^{3}b^{19}\times 3^{5}a^{10}\left(b^{2}\right)^{5}$$

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

$$27a^{3}b^{19}\times 3^{5}a^{10}b^{10}$$

Calculate 3 to the power of 5 and get 243.

$$27a^{3}b^{19}\times 243a^{10}b^{10}$$

Multiply 27 and 243 to get 6561.

$$6561a^{3}b^{19}a^{10}b^{10}$$

To multiply powers of the same base, add their exponents. Add 3 and 10 to get 13.

$$6561a^{13}b^{19}b^{10}$$

To multiply powers of the same base, add their exponents. Add 19 and 10 to get 29.

$$6561a^{13}b^{29}$$