Solve (3a^{2}b^5)^3*(ab^4)^2

$$( 3 a ^ { 2 } b ^ { 5 } ) ^ { 3 } \times ( a b ^ { 4 } ) ^ { 2 }$$

Evaluate

$$27a^{8}b^{23}$$

Solution Steps

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

$$3^{3}\left(a^{2}\right)^{3}\left(b^{5}\right)^{3}\left(ab^{4}\right)^{2}$$

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

$$3^{3}a^{6}\left(b^{5}\right)^{3}\left(ab^{4}\right)^{2}$$

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

$$3^{3}a^{6}b^{15}\left(ab^{4}\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$27a^{6}b^{15}\left(ab^{4}\right)^{2}$$

Expand \left(ab^{4}\right)^{2}.

$$27a^{6}b^{15}a^{2}\left(b^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$27a^{6}b^{15}a^{2}b^{8}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$27a^{8}b^{15}b^{8}$$

To multiply powers of the same base, add their exponents. Add 15 and 8 to get 23.

$$27a^{8}b^{23}$$

Expand

$$27a^{8}b^{23}$$

Solution Steps

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

$$3^{3}\left(a^{2}\right)^{3}\left(b^{5}\right)^{3}\left(ab^{4}\right)^{2}$$

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

$$3^{3}a^{6}\left(b^{5}\right)^{3}\left(ab^{4}\right)^{2}$$

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

$$3^{3}a^{6}b^{15}\left(ab^{4}\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$27a^{6}b^{15}\left(ab^{4}\right)^{2}$$

Expand \left(ab^{4}\right)^{2}.

$$27a^{6}b^{15}a^{2}\left(b^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$27a^{6}b^{15}a^{2}b^{8}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$27a^{8}b^{15}b^{8}$$

To multiply powers of the same base, add their exponents. Add 15 and 8 to get 23.

$$27a^{8}b^{23}$$