Question

4th period- integrated math 3 25/26
homework: homework #42
question list
use the quotient rule to simplify the expression. use positive
\\(\frac{8^{5}x^{6}}{8^{8}x^{4}}\\)
\\(\frac{8^{5}x^{6}}{8^{8}x^{4}} = \square\\)
question 27
question 28
question 29

Explanation:

Step1: Apply quotient rule for exponents

The quotient rule for exponents states that $\frac{a^m}{a^n} = a^{m - n}$ for the same base \(a\). We apply this to the bases \(8\) and \(x\) separately.

For the base \(8\): We have \(8^5\) in the numerator and \(8^8\) in the denominator. Using the quotient rule, \(8^{5 - 8}=8^{-3}\).

For the base \(x\): We have \(x^6\) in the numerator and \(x^4\) in the denominator. Using the quotient rule, \(x^{6 - 4}=x^{2}\).

So now our expression is \(8^{-3}x^{2}\).

Step2: Convert negative exponent to positive

A negative exponent rule states that \(a^{-n}=\frac{1}{a^n}\). So \(8^{-3}=\frac{1}{8^3}\).

Calculate \(8^3 = 8\times8\times8=512\).

So the expression becomes \(\frac{x^{2}}{8^{3}}=\frac{x^{2}}{512}\).

Answer:

\(\dfrac{x^{2}}{512}\)