Question
Simplify. Express your answer as a single term using exponents.
914^8 914^6/914^78
914^8 914^6/914^78
Answers
GPT-4o mini
To simplify the expression \( \frac{914^8 \cdot 914^6}{914^{78}} \), we can use the properties of exponents.
First, we can combine the exponents in the numerator:
\[
914^8 \cdot 914^6 = 914^{8+6} = 914^{14}
\]
Now, we rewrite the expression:
\[
\frac{914^{14}}{914^{78}}
\]
Next, we apply the property of exponents that says \( \frac{a^m}{a^n} = a^{m-n} \):
\[
\frac{914^{14}}{914^{78}} = 914^{14 - 78} = 914^{-64}
\]
Thus, the simplified form of the expression is:
\[
\boxed{914^{-64}}
\]
First, we can combine the exponents in the numerator:
\[
914^8 \cdot 914^6 = 914^{8+6} = 914^{14}
\]
Now, we rewrite the expression:
\[
\frac{914^{14}}{914^{78}}
\]
Next, we apply the property of exponents that says \( \frac{a^m}{a^n} = a^{m-n} \):
\[
\frac{914^{14}}{914^{78}} = 914^{14 - 78} = 914^{-64}
\]
Thus, the simplified form of the expression is:
\[
\boxed{914^{-64}}
\]