Question

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

Answer 1

Answer:

• $5x^6$

Explanation:

The expression that you want to simplify is:

• $5x\times \frac{1}{x^{-7}}\times x^{-2$

This is the simplification step-by-step:

1. Mulitply the expressions on the numerator among them and the expressions on the denominator among them:

$5x\times \frac{1}{x^{-7}}\times x^{-2}=\frac{5x\cdot x^{-2}}{x^{-7}}$

2. For equal bases that are multiplying, add the exponents:

$\frac{5x\cdot x^{-2}}{x^{-7}}=\frac{5x^{1-2}}{x^{-7}}=\frac{5x^{-1}}{x^{-7}}$

3. Pass the power on the denominator to the numerator by changing its sign (negative exponents become positive when inverted)

$\frac{5x^{-1}}{x^{-7}}=5x^{-1}x^{7}$

4. Simplify adding the exponents with the same base:

$5x^{-1}x^{7}=5x^{-1+7}=5x^6$

And that is the final expression in its most simple form.