Questions: 6^-8 * 6^5

Solution Steps

To solve the expression \(6^{-8} \cdot 6^{5}\), we can use the properties of exponents. Specifically, we can use the rule that \(a^m \cdot a^n = a^{m+n}\). By applying this rule, we can combine the exponents and then evaluate the result.

We start with the expression \(6^{-8} \cdot 6^{5}\). Using the property of exponents \(a^m \cdot a^n = a^{m+n}\), we combine the exponents: \[ 6^{-8} \cdot 6^{5} = 6^{-8 + 5} = 6^{-3} \]

Next, we evaluate \(6^{-3}\). This can be rewritten using the property of negative exponents: \[ 6^{-3} = \frac{1}{6^{3}} = \frac{1}{216} \]

Calculating the decimal value of \(\frac{1}{216}\) gives approximately \(0.004629629629629629\). Rounding this to four significant digits, we have: \[ 0.0046 \]

Final Answer