The process of rewriting utilizing negative exponents is essentially the conversion of expressions with positive exponents into their inverse forms with negative exponents. This is grounded in the fundamental principle of a^-n = 1/a^n, where "a" represents the base and "n" is indicative of the exponent. This principle streamlines the simplification of expressions and the resolution of equations effectively.
| Topic | Problem | Solution |
|---|---|---|
| None | Simplify the polynomial expression \(\frac{x^5}{x… | First, we apply the division rule of exponents, which says that \(\frac{a^n}{a^m} = a^{n-m}\). So t… |
| None | Simplify the given mathematical expression: $\fr… | The given mathematical expression is \(\frac{18 x^{3} y^{2}+9 x^{2} y^{5}}{3 x^{3} y^{2}}\). |
| None | Simplify the expression: $\frac{(x-3)^{2}}{x} \d… | Rewrite the division as multiplication: \(\frac{(x-3)^{2}}{x} \times \frac{2 x}{x^{2}-9}\) |
| None | Simplify the expression. First use the distributi… | Simplify the expression. First use the distributive property to remove parentheses: \(-5(4 x-3 y+4)… |
| None | Simplify the given expression: 10. $\frac{1}{3}(… | Distribute the fractions in each term over the binomial: \(\frac{1}{3}(12x-21)\) becomes \(4x-7\) a… |
| None | Simplify the given expression: $\frac{x^{45}}{y^… | Rewrite the given expression: \(\frac{x^{45}}{y^{4}} \div -\frac{2 x^{9}}{y^{39}}\) as multiplicati… |
| None | Question Fully simplify using only positive expon… | Given the expression \(\frac{5 x^{7} y^{5}}{10 x y^{3}}\) |