Solve [frac{(2rs^{3}p^{2})^{3}}{(rsp)^{6}}][frac{(r^{3}s^{2}p^2)^3}{4rs^2p^2}]=

$$[ \frac { ( 2 r s ^ { 3 } p ^ { 2 } ) ^ { 3 } } { ( r s p ) ^ { 6 } } ] [ \frac { ( r ^ { 3 } s ^ { 2 } p ^ { 2 } ) ^ { 3 } } { 4 r s ^ { 2 } p ^ { 2 } } ] =$$

Evaluate

$$2p^{4}r^{5}s^{7}$$

Solution Steps

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

$$\frac{2^{3}r^{3}\left(s^{3}\right)^{3}\left(p^{2}\right)^{3}}{\left(rsp\right)^{6}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{2^{3}r^{3}s^{9}\left(p^{2}\right)^{3}}{\left(rsp\right)^{6}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{2^{3}r^{3}s^{9}p^{6}}{\left(rsp\right)^{6}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8r^{3}s^{9}p^{6}}{\left(rsp\right)^{6}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

Expand \left(rsp\right)^{6}.

$$\frac{8r^{3}s^{9}p^{6}}{r^{6}s^{6}p^{6}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

Cancel out r^{3}p^{6}s^{6} in both numerator and denominator.

$$\frac{8s^{3}}{r^{3}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{8s^{3}}{r^{3}}\times \frac{\left(r^{3}\right)^{3}\left(s^{2}\right)^{3}\left(p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{8s^{3}}{r^{3}}\times \frac{r^{9}\left(s^{2}\right)^{3}\left(p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{8s^{3}}{r^{3}}\times \frac{r^{9}s^{6}\left(p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{8s^{3}}{r^{3}}\times \frac{r^{9}s^{6}p^{6}}{4rs^{2}p^{2}}$$

Cancel out rp^{2}s^{2} in both numerator and denominator.

$$\frac{8s^{3}}{r^{3}}\times \frac{p^{4}s^{4}r^{8}}{4}$$

Multiply \frac{8s^{3}}{r^{3}} times \frac{p^{4}s^{4}r^{8}}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8s^{3}p^{4}s^{4}r^{8}}{r^{3}\times 4}$$

Cancel out 4r^{3} in both numerator and denominator.

$$2s^{3}p^{4}s^{4}r^{5}$$

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

$$2s^{7}p^{4}r^{5}$$

Expand

$$2p^{4}r^{5}s^{7}$$

Solution Steps

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

$$\frac{2^{3}r^{3}\left(s^{3}\right)^{3}\left(p^{2}\right)^{3}}{\left(rsp\right)^{6}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{2^{3}r^{3}s^{9}\left(p^{2}\right)^{3}}{\left(rsp\right)^{6}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{2^{3}r^{3}s^{9}p^{6}}{\left(rsp\right)^{6}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8r^{3}s^{9}p^{6}}{\left(rsp\right)^{6}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

Expand \left(rsp\right)^{6}.

$$\frac{8r^{3}s^{9}p^{6}}{r^{6}s^{6}p^{6}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

Cancel out r^{3}p^{6}s^{6} in both numerator and denominator.

$$\frac{8s^{3}}{r^{3}}\times \frac{\left(r^{3}s^{2}p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{8s^{3}}{r^{3}}\times \frac{\left(r^{3}\right)^{3}\left(s^{2}\right)^{3}\left(p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{8s^{3}}{r^{3}}\times \frac{r^{9}\left(s^{2}\right)^{3}\left(p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{8s^{3}}{r^{3}}\times \frac{r^{9}s^{6}\left(p^{2}\right)^{3}}{4rs^{2}p^{2}}$$

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

$$\frac{8s^{3}}{r^{3}}\times \frac{r^{9}s^{6}p^{6}}{4rs^{2}p^{2}}$$

Cancel out rp^{2}s^{2} in both numerator and denominator.

$$\frac{8s^{3}}{r^{3}}\times \frac{p^{4}s^{4}r^{8}}{4}$$

Multiply \frac{8s^{3}}{r^{3}} times \frac{p^{4}s^{4}r^{8}}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8s^{3}p^{4}s^{4}r^{8}}{r^{3}\times 4}$$

Cancel out 4r^{3} in both numerator and denominator.

$$2s^{3}p^{4}s^{4}r^{5}$$

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

$$2s^{7}p^{4}r^{5}$$