a=(2^x), b=(2^y), express (2)^(x+2y) in terms of a and b,

Given the values \( a = 2^x \) and \( b = 2^y \), we want to express \( 2^{x+2y} \) in terms of \( a \) and \( b \).

### Solution:

\[
2^{x+2y} = 2^x \cdot 2^{2y}
\]

Since \( a = 2^x \) and \( b = 2^y \), we can substitute these into the equation:

\[
2^{x+2y} = a \cdot (2^y)^2
\]

Since \( 2^y = b \), we have:

\[
2^{x+2y} = a \cdot b^2
\]

Thus, the expression for \( 2^{x+2y} \) in terms of \( a \) and \( b \) is:

\[
2^{x+2y} = a \cdot b^2
\]

---

Would you like further details or have any questions? Here are 5 related questions:

1. How would you express \( 2^{3x + y} \) in terms of \( a \) and \( b \)?
2. What if \( a = 3^x \) and \( b = 3^y \)? How would \( 3^{x + 2y} \) be written?
3. How can the general expression \( 2^{kx + ly} \) be written in terms of \( a \) and \( b \)?
4. How does this approach change if the base is a different number, like 3 or 5?
5. Can you generalize the method for any exponential function \( n^{x + ky} \)?

**Tip:** When dealing with exponents, remember the properties of exponents, such as \( a^m \cdot a^n = a^{m+n} \) and \( (a^m)^n = a^{mn} \), as they simplify expressions greatly.

a=(2^x), b=(2^y), express (2)^(x+2y) in terms of a and b

Learn how to express 2^(x+2y) in terms of a and b using the properties of exponents. This problem involves key algebraic concepts, including the laws of exponents and substitutions. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation