Exponents signify how many times a given number, known as the base, is used in multiplication with itself. For example, 2^3 implies that 2 is multiplied by itself three times (2*2*2). On the other hand, negative exponents like 2^-3 indicate that the base is divided rather than multiplied. The use of exponents streamlines mathematical equations and computations.
| Topic | Problem | Solution |
|---|---|---|
| None | c. $6 \times 10^{-7}=\square=$ (Type an integer o… | The question is asking for the decimal representation of the scientific notation $6 \times 10^{-7}$. |
| None | 2) $2 \times 10^{3}+4 \times 10^{3}=$ | Calculate the sum of \(2 \times 10^{3}\) and \(4 \times 10^{3}\). |
| None | $5^{6} \cdot 5^{2} \cdot 5^{3}$ | Multiply the numbers with the same base and add the exponents: \(5^{6} \cdot 5^{2} \cdot 5^{3} = 5^… |
| None | \( \sqrt{8} \) | \( \sqrt{8} = \sqrt{4 \cdot 2} \) |
| None | \( \left(-\frac{2}{3}\right)^{2} \) | \(\left(-\frac{2}{3}\right)^{2} = (-1)^{2}\left(\frac{2}{3}\right)^{2}\) |