Solve x*(7^8)^9=(7^14)^5

$$x \cdot ( 7 ^ { 8 } ) ^ { 9 } = ( 7 ^ { 14 } ) ^ { 5 }$$

Solve for x

$$x=\frac{1}{49}\approx 0.020408163$$

Steps for Solving Linear Equation

To raise a power to another power, multiply the exponents. Multiply 8 and 9 to get 72.

$$x\times 7^{72}=\left(7^{14}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 14 and 5 to get 70.

$$x\times 7^{72}=7^{70}$$

Calculate 7 to the power of 72 and get 7031676478883553279994550741476882515263791803223057265323201.

$$x\times 7031676478883553279994550741476882515263791803223057265323201=7^{70}$$

Calculate 7 to the power of 70 and get 143503601609868434285603076356671071740077383739246066639249.

$$x\times 7031676478883553279994550741476882515263791803223057265323201=143503601609868434285603076356671071740077383739246066639249$$

Divide both sides by 7031676478883553279994550741476882515263791803223057265323201.

$$x=\frac{143503601609868434285603076356671071740077383739246066639249}{7031676478883553279994550741476882515263791803223057265323201}$$

Reduce the fraction \frac{143503601609868434285603076356671071740077383739246066639249}{7031676478883553279994550741476882515263791803223057265323201} to lowest terms by extracting and canceling out 143503601609868434285603076356671071740077383739246066639249.

$$x=\frac{1}{49}$$