Question

which expression does not simplify to 1?
\\(\frac{g^3}{g cdot g cdot g}\\) \\(\frac{gh^2}{h^2g}\\)
\\(\frac{g^4h^2}{gh^0}\\) \\(\frac{g cdot g}{g^2}\\)

Explanation:

Step1: Analyze $\frac{g^3}{g \cdot g \cdot g}$

Simplify denominator: $g \cdot g \cdot g = g^3$. Then $\frac{g^3}{g^3} = 1$.

Step2: Analyze $\frac{gh^2}{h^2g}$

Rearrange terms: $\frac{g}{g} \cdot \frac{h^2}{h^2} = 1 \cdot 1 = 1$.

Step3: Analyze $\frac{g^4h^2}{gh^0}$

Simplify $h^0 = 1$. Then use exponent rules: $\frac{g^4}{g} = g^{4 - 1} = g^3$, $\frac{h^2}{1} = h^2$. So $\frac{g^4h^2}{gh^0} = g^3h^2
eq 1$.

Step4: Analyze $\frac{g \cdot g}{g^2}$

Simplify numerator: $g \cdot g = g^2$. Then $\frac{g^2}{g^2} = 1$.

Answer:

$\boldsymbol{\frac{g^4h^2}{gh^0}}$ (the third option)