Question

1. simplify the expression. write your answer using only positive exponents. \\(\frac{3q}{4^{-2}} = \square\\)

Explanation:

Step1: Recall the negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) (or \(\frac{1}{a^{-n}} = a^{n}\) when moving from denominator to numerator). So we can rewrite \(4^{-2}\) in the denominator as \(4^{2}\) in the numerator by using the rule \(\frac{1}{a^{-n}}=a^{n}\).
Given the expression \(\frac{3q}{4^{-2}}\), applying the negative exponent rule to \(4^{-2}\), we get \(\frac{3q}{4^{-2}}=3q\times4^{2}\)

Step2: Calculate \(4^{2}\)

We know that \(4^{2}=4\times4 = 16\)

Step3: Multiply the terms

Now multiply \(3q\) by \(16\), so \(3q\times16 = 48q\)

Answer:

\(48q\)