3 answers
According to the properties of exponents, any non-zero number raised to the power of 0 is equal to 1. Therefore, the expression \((15^{-3} \cdot 4^{7})^0\) can be simplified as follows:
\[ (15^{-3} \cdot 4^{7})^0 = 1 \]
Since the base is raised to the power of 0, the entire expression evaluates to 1, regardless of the values of 15 and 4 (as long as they are not equal to zero).
Thus, the equivalent expression is:
\[ 1 \]
I apologize for the misunderstanding. Let's re-evaluate the expression \((15^{-3} \cdot 4^{7})^0\).
Since any non-zero expression raised to the power of 0 equals 1, the expression simplifies directly to 1. However, you mentioned that the answers are fractions, so you might be looking for representing it differently based on the components of the expression.
Given the original expression:
\[ (15^{-3} \cdot 4^{7})^0 = 1 \]
Given that \(15^{-3}\) as a fraction is \(\frac{1}{15^3}\) and \(4^7\) expressed as a fraction might be \(\frac{4^7}{1}\), the original components of the expression don't influence the outcome because of the exponent of 0.
Thus, while \((15^{-3} \cdot 4^{7})^0\) indeed simplifies to 1, those components do not need to be represented. However, if you are looking for the component forms, knowing that \(15^{-3}\) is technically a fraction, it is included in the context leading to:
\[ ( \frac{1}{15^3} \cdot 4^7 )^0 = 1 \]
But by properties of exponents, in any valid context, the entire expression equals 1.
Please clarify if you're expecting a different type of fraction representation involving the given bases, or if there's specific context that I'm missing regarding the fractional forms you're looking for.
