Question

Look at pic and answer pls

Answer 1

(a)  $x^{-5}$

(b)  $3x^{-7}$

(c)  $\frac{4}{3}x^4$

Solution:

To write each of the given expression in the form $ax^n$:

(a)  $\frac{x^3}{x^8}$

Using exponential rule: $\frac{a^x}{a^y}=a^{x-y}$

$\frac{x^3}{x^8}=x^{3-8}$

$\frac{x^3}{x^8}=x^{-5}$

(b) $\frac{6x}{2x^8}$

Divide numerator and denominator by the common factor 2, we get

$\frac{6x}{2x^8}=\frac{3x}{x^8}$

Using exponential rule: $\frac{a^x}{a^y}=a^{x-y}$

      $=3x^{1-8}$

$\frac{6x}{2x^8} =3x^{-7}$

(c)  $\frac{28x^6}{21x^2}$

Divide numerator and denominator by the common factor 7, we get

$\frac{28x^6}{21x^2}=\frac{4x^6}{3x^2}$

Using exponential rule: $\frac{a^x}{a^y}=a^{x-y}$

        $=\frac{4}{3}x^{6-2}$

$\frac{28x^6}{21x^2}=\frac{4}{3}x^4$