Solve (4a^{9}b)^2(5a^6b^7)^3

$$( 4 a ^ { 9 } b ) ^ { 2 } ( 5 a ^ { 6 } b ^ { 7 } ) ^ { 3 }$$

Evaluate

$$2000b^{23}a^{36}$$

Solution Steps

Expand \left(4a^{9}b\right)^{2}.

$$4^{2}\left(a^{9}\right)^{2}b^{2}\times \left(5a^{6}b^{7}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$4^{2}a^{18}b^{2}\times \left(5a^{6}b^{7}\right)^{3}$$

Calculate 4 to the power of 2 and get 16.

$$16a^{18}b^{2}\times \left(5a^{6}b^{7}\right)^{3}$$

Expand \left(5a^{6}b^{7}\right)^{3}.

$$16a^{18}b^{2}\times 5^{3}\left(a^{6}\right)^{3}\left(b^{7}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$16a^{18}b^{2}\times 5^{3}a^{18}\left(b^{7}\right)^{3}$$

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

$$16a^{18}b^{2}\times 5^{3}a^{18}b^{21}$$

Calculate 5 to the power of 3 and get 125.

$$16a^{18}b^{2}\times 125a^{18}b^{21}$$

Multiply 16 and 125 to get 2000.

$$2000a^{18}b^{2}a^{18}b^{21}$$

To multiply powers of the same base, add their exponents. Add 18 and 18 to get 36.

$$2000a^{36}b^{2}b^{21}$$

To multiply powers of the same base, add their exponents. Add 2 and 21 to get 23.

$$2000a^{36}b^{23}$$

Expand

$$2000b^{23}a^{36}$$

Solution Steps

Expand \left(4a^{9}b\right)^{2}.

$$4^{2}\left(a^{9}\right)^{2}b^{2}\times \left(5a^{6}b^{7}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$4^{2}a^{18}b^{2}\times \left(5a^{6}b^{7}\right)^{3}$$

Calculate 4 to the power of 2 and get 16.

$$16a^{18}b^{2}\times \left(5a^{6}b^{7}\right)^{3}$$

Expand \left(5a^{6}b^{7}\right)^{3}.

$$16a^{18}b^{2}\times 5^{3}\left(a^{6}\right)^{3}\left(b^{7}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$16a^{18}b^{2}\times 5^{3}a^{18}\left(b^{7}\right)^{3}$$

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

$$16a^{18}b^{2}\times 5^{3}a^{18}b^{21}$$

Calculate 5 to the power of 3 and get 125.

$$16a^{18}b^{2}\times 125a^{18}b^{21}$$

Multiply 16 and 125 to get 2000.

$$2000a^{18}b^{2}a^{18}b^{21}$$

To multiply powers of the same base, add their exponents. Add 18 and 18 to get 36.

$$2000a^{36}b^{2}b^{21}$$

To multiply powers of the same base, add their exponents. Add 2 and 21 to get 23.

$$2000a^{36}b^{23}$$