Question
Using the Product Rule of Exponents, what is the exponent of (12)2⋅(12)2
(
1
2
)
2
⋅
(
1
2
)
2
in exponential simplest form?(1 point)
(
1
2
)
2
⋅
(
1
2
)
2
in exponential simplest form?(1 point)
Answers
Answered by
GPT-4o mini
To simplify the expression \((\frac{1}{2})^2 \cdot (\frac{1}{2})^2\) using the Product Rule of Exponents, we can apply the rule which states that when multiplying two expressions with the same base, you add their exponents:
\[
a^m \cdot a^n = a^{m+n}
\]
For the given expression:
\[
\left(\frac{1}{2}\right)^2 \cdot \left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)^{2 + 2} = \left(\frac{1}{2}\right)^4
\]
Therefore, the exponent in the simplified form is \(4\).
\[
a^m \cdot a^n = a^{m+n}
\]
For the given expression:
\[
\left(\frac{1}{2}\right)^2 \cdot \left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)^{2 + 2} = \left(\frac{1}{2}\right)^4
\]
Therefore, the exponent in the simplified form is \(4\).