Solve 2p^2q*(3pq^3)^2divpq^-4

$$2 p ^ { 2 } q \times ( 3 p q ^ { 3 } ) ^ { 2 } \div p q ^ { - 4 }$$

Evaluate

$$18\left(pq\right)^{3}$$

Solution Steps

Cancel out p in both numerator and denominator.

$$2pq\times \left(3pq^{3}\right)^{2}q^{-4}$$

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

$$2pq\times 3^{2}p^{2}\left(q^{3}\right)^{2}q^{-4}$$

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

$$2pq\times 3^{2}p^{2}q^{6}q^{-4}$$

Calculate 3 to the power of 2 and get 9.

$$2pq\times 9p^{2}q^{6}q^{-4}$$

Multiply 2 and 9 to get 18.

$$18pqp^{2}q^{6}q^{-4}$$

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

$$18p^{3}qq^{6}q^{-4}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$18p^{3}q^{7}q^{-4}$$

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

$$18p^{3}q^{3}$$

Expand

$$18\left(pq\right)^{3}$$

Solution Steps

Cancel out p in both numerator and denominator.

$$2pq\times \left(3pq^{3}\right)^{2}q^{-4}$$

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

$$2pq\times 3^{2}p^{2}\left(q^{3}\right)^{2}q^{-4}$$

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

$$2pq\times 3^{2}p^{2}q^{6}q^{-4}$$

Calculate 3 to the power of 2 and get 9.

$$2pq\times 9p^{2}q^{6}q^{-4}$$

Multiply 2 and 9 to get 18.

$$18pqp^{2}q^{6}q^{-4}$$

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

$$18p^{3}qq^{6}q^{-4}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$18p^{3}q^{7}q^{-4}$$

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

$$18p^{3}q^{3}$$