Math Problem Statement

2^3x-2^-3x

Solution

The expression you've provided is 23x23x2^{3x} - 2^{-3x}.

This is an exponential expression involving powers of 2, where the exponents depend on xx.

Step-by-step breakdown:

  • 23x2^{3x} means 22 raised to the power of 3x3x.
  • 23x2^{-3x} means 22 raised to the power of 3x-3x, which can also be written as 123x\frac{1}{2^{3x}}.

So, the expression is:

23x123x2^{3x} - \frac{1}{2^{3x}}

This expression is already in a simplified form, but if you want to explore further or have a specific value of xx, you can substitute that value to evaluate the expression.

Would you like to solve it for a specific value of xx, or do you need further clarification on how to approach this?

Here are 5 related questions:

  1. What happens if you set x=1x = 1?
  2. How do you simplify expressions with both positive and negative exponents?
  3. Can this expression be written in terms of a hyperbolic sine function?
  4. What is the derivative of 23x23x2^{3x} - 2^{-3x} with respect to xx?
  5. How can you graph the expression 23x23x2^{3x} - 2^{-3x}?

Tip:

When dealing with negative exponents, remember that an=1ana^{-n} = \frac{1}{a^n}.

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Math Problem Analysis

Mathematical Concepts

Exponents
Algebra
Exponential Expressions

Formulas

a^(-n) = 1 / a^n

Theorems

Exponent rules for positive and negative exponents

Suitable Grade Level

Grades 9-11