in 4 - 7, use inverse operations to find the value of the variable needed to make the equation true. 4…

Explanation:

Step1: Recall inverse - square operation

The inverse operation of squaring a number is taking the square - root. For the equation $x^{2}=169$, we have $x=\pm\sqrt{169}$. Since $\sqrt{169} = 13$, then $x=\pm13$.

Step2: Recall inverse - cube operation

For the equation $b^{3}=343$, the inverse operation of cubing a number is taking the cube - root. So $b = \sqrt[3]{343}$. Since $7\times7\times7=343$, then $b = 7$.

Step3: Recall inverse - square operation

For the equation $n^{2}=625$, we take the square - root of both sides. So $n=\pm\sqrt{625}$. Since $\sqrt{625}=25$, then $n=\pm25$.

Step4: Recall inverse - cube operation

For the equation $a^{3}=1000$, we take the cube - root of both sides. So $a=\sqrt[3]{1000}$. Since $10\times10\times10 = 1000$, then $a = 10$.

Answer:

4. $x=\pm13$
5. $b = 7$
6. $n=\pm25$
7. $a = 10$