Question

Rewrite the expression with positive exponents $$\frac{1}{(4 x)^{-5}}$$

Short answer

The expression \(\frac{1}{(4 x)^{-5}}\) rewritten with positive exponents is \((4x)^5\).

Step-by-step solution

Identify the term with a negative exponent

In our expression, \((4x)^{-5}\) is the term with a negative exponent - this is the term we want to rewrite so the exponent is positive.

Apply the rules of exponents

One of the fundamental rules of exponents is that \( a^{-n} = \frac{1}{a^n} \). We can apply this rule to our expression to change the negative exponent to a positive exponent. Hence, \((4x)^{-5} = \frac{1}{(4x)^5}\). The expression now becomes \(\frac{1}{\frac{1}{(4x)^5}}\).

Simplify the expression

In mathematics, \(\frac{a}{\frac{b}{c}}\) is equivalent to \(a \cdot \frac{c}{b}\). So we can simplify our expression to \((4x)^5\).