Question
Apply the Properties of Integer Exponents to generate equivalent expressions to (14 to the power of 3⋅27 to the power of−7) to the power of 0/ 3 to the power of 4
with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(14 to the power of 3 ⋅ 27 to the power of −7) to the power of 0 / 3 to the power of 4=
with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(14 to the power of 3 ⋅ 27 to the power of −7) to the power of 0 / 3 to the power of 4=
Answers
GPT-4o mini
To apply the properties of integer exponents, let's first simplify the expression step-by-step.
1. **Understanding the expression**:
\[
\frac{(14^3 \cdot 27^{-7})^0}{3^4}
\]
2. **Simplifying the power of zero**:
According to the property of exponents, any non-zero number raised to the power of zero is 1. Therefore:
\[
(14^3 \cdot 27^{-7})^0 = 1
\]
3. **Now, the expression simplifies to**:
\[
\frac{1}{3^4}
\]
4. **Calculating \(3^4\)**:
\[
3^4 = 3 \cdot 3 \cdot 3 \cdot 3 = 81
\]
5. **Constructing the final expression**:
\[
\frac{1}{3^4} = \frac{1}{81}
\]
Thus, the final simplified fraction, with no remaining exponents, is:
\[
\boxed{\frac{1}{81}}
\]
1. **Understanding the expression**:
\[
\frac{(14^3 \cdot 27^{-7})^0}{3^4}
\]
2. **Simplifying the power of zero**:
According to the property of exponents, any non-zero number raised to the power of zero is 1. Therefore:
\[
(14^3 \cdot 27^{-7})^0 = 1
\]
3. **Now, the expression simplifies to**:
\[
\frac{1}{3^4}
\]
4. **Calculating \(3^4\)**:
\[
3^4 = 3 \cdot 3 \cdot 3 \cdot 3 = 81
\]
5. **Constructing the final expression**:
\[
\frac{1}{3^4} = \frac{1}{81}
\]
Thus, the final simplified fraction, with no remaining exponents, is:
\[
\boxed{\frac{1}{81}}
\]