Solve (25/36)^{3}*frac{42^{3}*24^4}{140^2}=10^7*y^1

$$( \frac { 25 } { 36 } ) ^ { 3 } \times \frac { 42 ^ { 3 } \times 24 ^ { 4 } } { 140 ^ { 2 } } = 10 ^ { 7 } \times y ^ { 1 }$$

Solve for y

$$y=\frac{21}{500}=0.042$$

Steps for Solving Linear Equation

Calculate \frac{25}{36} to the power of 3 and get \frac{15625}{46656}.

$$\frac{15625}{46656}\times \frac{42^{3}\times 24^{4}}{140^{2}}=10^{7}y^{1}$$

Calculate 42 to the power of 3 and get 74088.

$$\frac{15625}{46656}\times \frac{74088\times 24^{4}}{140^{2}}=10^{7}y^{1}$$

Calculate 24 to the power of 4 and get 331776.

$$\frac{15625}{46656}\times \frac{74088\times 331776}{140^{2}}=10^{7}y^{1}$$

Multiply 74088 and 331776 to get 24580620288.

$$\frac{15625}{46656}\times \frac{24580620288}{140^{2}}=10^{7}y^{1}$$

Calculate 140 to the power of 2 and get 19600.

$$\frac{15625}{46656}\times \frac{24580620288}{19600}=10^{7}y^{1}$$

Reduce the fraction \frac{24580620288}{19600} to lowest terms by extracting and canceling out 784.

$$\frac{15625}{46656}\times \frac{31352832}{25}=10^{7}y^{1}$$

Multiply \frac{15625}{46656} and \frac{31352832}{25} to get 420000.

$$420000=10^{7}y^{1}$$

Calculate 10 to the power of 7 and get 10000000.

$$420000=10000000y^{1}$$

Calculate y to the power of 1 and get y.

$$420000=10000000y$$

Swap sides so that all variable terms are on the left hand side.

$$10000000y=420000$$

Divide both sides by 10000000.

$$y=\frac{420000}{10000000}$$

Reduce the fraction \frac{420000}{10000000} to lowest terms by extracting and canceling out 20000.

$$y=\frac{21}{500}$$