Question

simplify. express your answer using positive exponents.\\(\frac{7d^{0}}{(7d^{-6})(d^{2})}\\)

Explanation:

Step1: Simplify the numerator's exponent

Recall that any non - zero number to the power of 0 is 1, so \(d^{0}=1\). Then the numerator \(7d^{0}=7\times1 = 7\).

Step2: Simplify the denominator

First, use the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\) for the terms with base \(d\) in the denominator. In the denominator \((7d^{-6})(d^{2})\), for the \(d\) terms: \(d^{-6}\times d^{2}=d^{-6 + 2}=d^{-4}\). And the coefficient is 7, so the denominator is \(7d^{-4}\).

Step3: Simplify the fraction

Now our expression is \(\frac{7}{7d^{-4}}\). The 7 in the numerator and denominator cancels out (since \(\frac{7}{7} = 1\)), so we have \(\frac{1}{d^{-4}}\).

Step4: Convert negative exponent to positive

Recall that \(\frac{1}{a^{-n}}=a^{n}\) (for \(a
eq0\) and \(n\) is an integer). So \(\frac{1}{d^{-4}}=d^{4}\).

Answer:

\(d^{4}\)