To write the number \(5.4 \times 10^{-65.4 \times 10^{-6}}\) in standard form, we start by first simplifying the exponent \( -65.4 \times 10^{-6} \).
Calculating \( -65.4 \times 10^{-6} \) results in: \[ -0.0000654 \]
Thus, the expression can now be rewritten in standard form as: \[ 5.4 \times 10^{-0.0000654} \]
Now, using the definition of standard form in decimal notation, we have:
\[ 5.4 \times 10^{-0.0000654} \text{ is essentially } 5.4 \times 10^{0} \text{ (approximately 1)} \]
Thus, the number can be represented approximately as:
\[ 5.4 \]
If you wanted the exact form, we would say it as \( 5.4 \times 10^{-0.0000654} \), which is already stated.
In conclusion, the standard form of \(5.4 \times 10^{-65.4 \times 10^{-6}}\) is approximately:
\[ 5.4 \]
However, due to the exponent being remarkably small, for practical purposes it remains \(5.4 \times 10^{0}\) and doesn't need further adjustment.