What is b? In this educational setting, we explore an interesting mathematical expression. The equation given in the image is:\[\sqrt{4^a} \cdot \sqrt{4^b} = 2^{b}\]Explanation: - The term \(\sqrt{4^a}\) represents the square root of \(4\) raised to the power of \(a\).- The term \(\sqrt{4^b}\) represents the square root of \(4\) raised to the power of \(b\).To further understand, let’s simplify both square root terms:\[\sqrt{4^a} = (\sqrt{4})^a = 2^a\]\[\sqrt{4^b} = (\sqrt{4})^b = 2^b\]Thus, the equation now becomes:\[2^a \cdot 2^b\]Using the properties of exponents, we know that:\[2^a \cdot 2^b = 2^{a+b}\]Therefore, the given equation can be simplified to:\[2^{a+b} = 2^b\]For the equality to hold true, \(a + b\) must be equal to \(b\). Therefore:\[a + b = b\]Subtract \(b\) from both sides:\[a = 0\]This shows that the simplest solution to the equation is when \(a = 0\). This mathematical expression is a good example of exploring the properties of exponents and square roots.

Name: What is b? In this educational setting, we explore an interesting math
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: What is b? In this educational setting, we explore an interesting mathematical expression. The equation given in the image is:\[\sqrt{4^a} \cdot \sqrt{4^b} = 2^{b}\]Explanation: - The term \(\sqrt{4^a}\) represents the square root of \(4\) raised to