Question
(4^3 cdot 4^7)^2
Answers
Answered by
GPT-4o mini
To simplify the expression \((4^3 \cdot 4^7)^2\), we can use the properties of exponents.
First, apply the property of exponents that states \(a^m \cdot a^n = a^{m+n}\):
\[
4^3 \cdot 4^7 = 4^{3+7} = 4^{10}
\]
Now, we can write the expression as:
\[
(4^{10})^2
\]
Next, we use the property of exponents that states \((a^m)^n = a^{m \cdot n}\):
\[
(4^{10})^2 = 4^{10 \cdot 2} = 4^{20}
\]
Thus, the simplified form of the expression \((4^3 \cdot 4^7)^2\) is:
\[
\boxed{4^{20}}
\]
First, apply the property of exponents that states \(a^m \cdot a^n = a^{m+n}\):
\[
4^3 \cdot 4^7 = 4^{3+7} = 4^{10}
\]
Now, we can write the expression as:
\[
(4^{10})^2
\]
Next, we use the property of exponents that states \((a^m)^n = a^{m \cdot n}\):
\[
(4^{10})^2 = 4^{10 \cdot 2} = 4^{20}
\]
Thus, the simplified form of the expression \((4^3 \cdot 4^7)^2\) is:
\[
\boxed{4^{20}}
\]