Solve (a^2b)^2*(ab^2)^3*(abc)

$$( a ^ { 2 } b ) ^ { 2 } \cdot ( a b ^ { 2 } ) ^ { 3 } \cdot ( a b c )$$

Evaluate

$$ca^{8}b^{9}$$

Solution Steps

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

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

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

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

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

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

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

$$a^{4}b^{2}a^{3}b^{6}abc$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$a^{7}b^{2}b^{6}abc$$

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

$$a^{7}b^{8}abc$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$a^{8}b^{8}bc$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$a^{8}b^{9}c$$

Expand

$$ca^{8}b^{9}$$

Solution Steps

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

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

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

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

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

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

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

$$a^{4}b^{2}a^{3}b^{6}abc$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$a^{7}b^{2}b^{6}abc$$

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

$$a^{7}b^{8}abc$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$a^{8}b^{8}bc$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$a^{8}b^{9}c$$