Question

simplify. express your answer using positive exponents.\\(h^{-1} \cdot h^{0} \cdot h^{0}\\)

Explanation:

Step1: Recall exponent rules (product of powers and zero exponent)

The product of powers rule states that \(a^m \cdot a^n = a^{m + n}\), and the zero exponent rule states that \(a^0=1\) for \(a
eq0\).

First, apply the zero exponent rule to \(h^0\): \(h^0 = 1\), so we have \(h^{-1}\cdot1\cdot1\). But also, we can use the product of powers rule directly on the exponents. Let's add the exponents of \(h\) since we are multiplying powers with the same base.

The exponents are \(- 1\), \(0\), and \(0\). So we calculate the sum of the exponents: \(-1+0 + 0=-1\). So the expression becomes \(h^{-1}\).

Step2: Convert negative exponent to positive

Using the rule \(a^{-n}=\frac{1}{a^n}\) for \(a
eq0\) and \(n>0\), we convert \(h^{-1}\) to \(\frac{1}{h}\).

Answer:

\(\frac{1}{h}\)