Simplify 5 x times the fraction 1 over x to the power of negative 7 times x to the power of negative 2. 5x 5x−6 5 5x6

Accepted Solution

Answer:[tex]5x^6[/tex]Explanation:The expression that you want to simplify is:[tex]5x\times \frac{1}{x^{-7}}\times x^{-2[/tex]This is the simplification step-by-step:1. Mulitply the expressions on the numerator among them and the expressions on the denominator among them:[tex]5x\times \frac{1}{x^{-7}}\times x^{-2}=\frac{5x\cdot x^{-2}}{x^{-7}}[/tex]2. For equal bases that are multiplying, add the exponents:[tex]\frac{5x\cdot x^{-2}}{x^{-7}}=\frac{5x^{1-2}}{x^{-7}}=\frac{5x^{-1}}{x^{-7}}[/tex]3. Pass the power on the denominator to the numerator by changing its sign (negative exponents become positive when inverted)[tex]\frac{5x^{-1}}{x^{-7}}=5x^{-1}x^{7}[/tex]4. Simplify adding the exponents with the same base:[tex]5x^{-1}x^{7}=5x^{-1+7}=5x^6[/tex]And that is the final expression in its most simple form.