Solve |x+frac{(7^{4})^{3}*7}{49^6}|=12^7*12^8/144^7

$$| x + \frac { ( 7 ^ { 4 } ) ^ { 3 } \cdot 7 } { 49 ^ { 6 } } | = \frac { 12 ^ { 7 } \cdot 12 ^ { 8 } } { 144 ^ { 7 } }$$

Solve for x

$$x=-19$$

$$x=5$$

Steps Using Definition of Absolute Value

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$|x+\frac{7^{12}\times 7}{49^{6}}|=\frac{12^{7}\times 12^{8}}{144^{7}}$$

To multiply powers of the same base, add their exponents. Add 12 and 1 to get 13.

$$|x+\frac{7^{13}}{49^{6}}|=\frac{12^{7}\times 12^{8}}{144^{7}}$$

To multiply powers of the same base, add their exponents. Add 7 and 8 to get 15.

$$|x+\frac{7^{13}}{49^{6}}|=\frac{12^{15}}{144^{7}}$$

Calculate 7 to the power of 13 and get 96889010407.

$$|x+\frac{96889010407}{49^{6}}|=\frac{12^{15}}{144^{7}}$$

Calculate 49 to the power of 6 and get 13841287201.

$$|x+\frac{96889010407}{13841287201}|=\frac{12^{15}}{144^{7}}$$

Divide 96889010407 by 13841287201 to get 7.

$$|x+7|=\frac{12^{15}}{144^{7}}$$

Calculate 12 to the power of 15 and get 15407021574586368.

$$|x+7|=\frac{15407021574586368}{144^{7}}$$

Calculate 144 to the power of 7 and get 1283918464548864.

$$|x+7|=\frac{15407021574586368}{1283918464548864}$$

Divide 15407021574586368 by 1283918464548864 to get 12.

$$|x+7|=12$$

Use the definition of absolute value.

$$x+7=12 x+7=-12$$

Subtract 7 from both sides of the equation.

$$x=5 x=-19$$