Question

question 1 (1 point) (03.01 mc) explain how the quotient of powers property was used to simplify this expression. 8/2^2 = 2^5 a by finding the quotient of the bases to be 1/4 and cancelling common factors b by finding the quotient of the bases to be 1/4 and simplifying the expression c by simplifying 8 to 2^3 to make both powers base two and subtracting the exponents d by simplifying 8 to 2^3 to make both powers base two and adding the exponents

Explanation:

Step1: Rewrite 8 as a power of 2

Since \(8 = 2^3\), the expression \(\frac{8}{2^5}\) becomes \(\frac{2^3}{2^5}\).

Step2: Apply quotient - of - powers rule

The quotient - of - powers rule states that \(\frac{a^m}{a^n}=a^{m - n}\) for \(a
eq0\). Here \(a = 2\), \(m = 3\) and \(n = 5\), so \(\frac{2^3}{2^5}=2^{3-5}=2^{-2}\).

Answer:

B. By finding the quotient of the bases to be 1 and simplifying the expression

(We first rewrite 8 as \(2^3\) to make both bases the same. Then we use the quotient - of - powers rule \(\frac{a^m}{a^n}=a^{m - n}\) to simplify the expression. This matches option B which correctly describes the process of using the quotient - of - powers property.)