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 | $\left[-4^{3}\right]^{-7}$ | \(-4^3 = -64\) |
| None | 11. Complete the table. [3] \begin{tabular}{|c|c|… | \(V(x) = 20(1.05)^x\) |
| None | b) $\left(\frac{-64}{27}\right)^{-\frac{1}{3}}=$ | Find the cube root of the given fraction: \(\sqrt[3]{\frac{-64}{27}}\) |
| None | Question 1 (1 point) When you multiply powers wit… | When multiplying powers with the same base, you add the exponents. This is a basic rule of exponent… |
| None | Which expression is equivalent to $5^{10} \cdot 5… | The question is asking for the equivalent expression of \(5^{10} \cdot 5^{5}\). |
| None | (2) Complete $\mathrm{com}>,<\mathrm{ou}=$. a) $1… | \(10^3 \leq 10^6 \Rightarrow \mathrm{com}>\) |
| None | Rewrite \[ \frac{1}{10,000,000} \] as a power of … | Rewrite the fraction as a power of 10: \(\frac{1}{10^7}\) |
| None | Change the exponential statement to an equivalent… | Given the exponential statement \(625=5^{4}\). |
| None | \( \frac{(-7)^{3} \times 7^{8} \times(-49)^{2}}{7… | \( \frac{(-7)^{3} \times 7^{8} \times(-49)^{2}}{7^{-4} \times\left(-7^{3}\right)^{5}} \) = \( \frac… |
| None | Find the cube root of \[ -27 \] that graphs in th… | \(z^3 = -27\) |