Questions: use the laws of exponents to simplify 81^4/81^3.75

Solution Steps

To simplify the given expression using the laws of exponents, we can use the property that \(\frac{a^m}{a^n} = a^{m-n}\). Here, we have the same base (81) in both the numerator and the denominator, so we can subtract the exponents.

We start with the expression: \[ \frac{81^4}{81^{3.75}} \]

Using the property \(\frac{a^m}{a^n} = a^{m-n}\), we subtract the exponents: \[ 81^{4 - 3.75} = 81^{0.25} \]

We need to calculate \(81^{0.25}\). Since \(81 = 3^4\), we have: \[ 81^{0.25} = (3^4)^{0.25} = 3^{4 \times 0.25} = 3^1 = 3 \]

Final Answer