Solve (3pr^{2})^2(5p^2r^3)^3

$$( 3 p r ^ { 2 } ) ^ { 2 } ( 5 p ^ { 2 } r ^ { 3 } ) ^ { 3 }$$

Evaluate

$$1125p^{8}r^{13}$$

Solution Steps

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

$$3^{2}p^{2}\left(r^{2}\right)^{2}\times \left(5p^{2}r^{3}\right)^{3}$$

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

$$3^{2}p^{2}r^{4}\times \left(5p^{2}r^{3}\right)^{3}$$

Calculate 3 to the power of 2 and get 9.

$$9p^{2}r^{4}\times \left(5p^{2}r^{3}\right)^{3}$$

Expand \left(5p^{2}r^{3}\right)^{3}.

$$9p^{2}r^{4}\times 5^{3}\left(p^{2}\right)^{3}\left(r^{3}\right)^{3}$$

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

$$9p^{2}r^{4}\times 5^{3}p^{6}\left(r^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$9p^{2}r^{4}\times 5^{3}p^{6}r^{9}$$

Calculate 5 to the power of 3 and get 125.

$$9p^{2}r^{4}\times 125p^{6}r^{9}$$

Multiply 9 and 125 to get 1125.

$$1125p^{2}r^{4}p^{6}r^{9}$$

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

$$1125p^{8}r^{4}r^{9}$$

To multiply powers of the same base, add their exponents. Add 4 and 9 to get 13.

$$1125p^{8}r^{13}$$

Expand

$$1125p^{8}r^{13}$$

Solution Steps

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

$$3^{2}p^{2}\left(r^{2}\right)^{2}\times \left(5p^{2}r^{3}\right)^{3}$$

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

$$3^{2}p^{2}r^{4}\times \left(5p^{2}r^{3}\right)^{3}$$

Calculate 3 to the power of 2 and get 9.

$$9p^{2}r^{4}\times \left(5p^{2}r^{3}\right)^{3}$$

Expand \left(5p^{2}r^{3}\right)^{3}.

$$9p^{2}r^{4}\times 5^{3}\left(p^{2}\right)^{3}\left(r^{3}\right)^{3}$$

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

$$9p^{2}r^{4}\times 5^{3}p^{6}\left(r^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$9p^{2}r^{4}\times 5^{3}p^{6}r^{9}$$

Calculate 5 to the power of 3 and get 125.

$$9p^{2}r^{4}\times 125p^{6}r^{9}$$

Multiply 9 and 125 to get 1125.

$$1125p^{2}r^{4}p^{6}r^{9}$$

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

$$1125p^{8}r^{4}r^{9}$$

To multiply powers of the same base, add their exponents. Add 4 and 9 to get 13.

$$1125p^{8}r^{13}$$