1. **State the problem:** We have the function $g(x) = a \times b^x$ where $a$ and $b$ are constants. We know $g(0) = 8$ and $g(3) = 343$. We need to find $g(1)$. 2. **Use the given information:** Since $g(0) = a \times b^0 = a \times 1 = a$, we have: $$a = 8$$ 3. **Use the second condition:** $$g(3) = a \times b^3 = 343$$ Substitute $a = 8$: $$8 \times b^3 = 343$$ 4. **Solve for $b^3$:** $$b^3 = \frac{343}{8}$$ Show cancellation: $$b^3 = \frac{\cancel{343}}{\cancel{8}}$$ (Here, no common factors to cancel, so fraction remains as is.) 5. **Simplify $b^3$:** Note that $343 = 7^3$ and $8 = 2^3$, so: $$b^3 = \frac{7^3}{2^3} = \left(\frac{7}{2}\right)^3$$ 6. **Take cube root to find $b$:** $$b = \frac{7}{2}$$ 7. **Find $g(1)$:** $$g(1) = a \times b^1 = 8 \times \frac{7}{2}$$ 8. **Simplify $g(1)$:** $$g(1) = 8 \times \frac{7}{2} = \frac{8 \times 7}{2} = \frac{56}{2}$$ Show cancellation: $$g(1) = \frac{\cancel{56}}{\cancel{2}} = 28$$ **Final answer:** $$g(1) = 28$$