Solve (p^{2}r^{2})^{4}(-7p^3r^4)^2(apr^3)

$$( p ^ { 2 } r ^ { 2 } ) ^ { 4 } ( - 7 p ^ { 3 } r ^ { 4 } ) ^ { 2 } ( a p r ^ { 3 } )$$

Evaluate

$$49ap^{15}r^{19}$$

Solution Steps

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

$$\left(p^{2}\right)^{4}\left(r^{2}\right)^{4}\left(-7p^{3}r^{4}\right)^{2}apr^{3}$$

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

$$p^{8}\left(r^{2}\right)^{4}\left(-7p^{3}r^{4}\right)^{2}apr^{3}$$

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

$$p^{8}r^{8}\left(-7p^{3}r^{4}\right)^{2}apr^{3}$$

Expand \left(-7p^{3}r^{4}\right)^{2}.

$$p^{8}r^{8}\left(-7\right)^{2}\left(p^{3}\right)^{2}\left(r^{4}\right)^{2}apr^{3}$$

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

$$p^{8}r^{8}\left(-7\right)^{2}p^{6}\left(r^{4}\right)^{2}apr^{3}$$

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

$$p^{8}r^{8}\left(-7\right)^{2}p^{6}r^{8}apr^{3}$$

Calculate -7 to the power of 2 and get 49.

$$p^{8}r^{8}\times 49p^{6}r^{8}apr^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$p^{14}r^{8}\times 49r^{8}apr^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 8 to get 16.

$$p^{14}r^{16}\times 49apr^{3}$$

To multiply powers of the same base, add their exponents. Add 14 and 1 to get 15.

$$p^{15}r^{16}\times 49ar^{3}$$

To multiply powers of the same base, add their exponents. Add 16 and 3 to get 19.

$$p^{15}r^{19}\times 49a$$

Expand

$$49ap^{15}r^{19}$$

Solution Steps

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

$$\left(p^{2}\right)^{4}\left(r^{2}\right)^{4}\left(-7p^{3}r^{4}\right)^{2}apr^{3}$$

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

$$p^{8}\left(r^{2}\right)^{4}\left(-7p^{3}r^{4}\right)^{2}apr^{3}$$

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

$$p^{8}r^{8}\left(-7p^{3}r^{4}\right)^{2}apr^{3}$$

Expand \left(-7p^{3}r^{4}\right)^{2}.

$$p^{8}r^{8}\left(-7\right)^{2}\left(p^{3}\right)^{2}\left(r^{4}\right)^{2}apr^{3}$$

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

$$p^{8}r^{8}\left(-7\right)^{2}p^{6}\left(r^{4}\right)^{2}apr^{3}$$

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

$$p^{8}r^{8}\left(-7\right)^{2}p^{6}r^{8}apr^{3}$$

Calculate -7 to the power of 2 and get 49.

$$p^{8}r^{8}\times 49p^{6}r^{8}apr^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$p^{14}r^{8}\times 49r^{8}apr^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 8 to get 16.

$$p^{14}r^{16}\times 49apr^{3}$$

To multiply powers of the same base, add their exponents. Add 14 and 1 to get 15.

$$p^{15}r^{16}\times 49ar^{3}$$

To multiply powers of the same base, add their exponents. Add 16 and 3 to get 19.

$$p^{15}r^{19}\times 49a$$