Simplifying an expression with exponents

In summary, an expression with exponents is a mathematical statement that includes variables, numbers, and exponents to represent repeated multiplication. To simplify such an expression, follow the order of operations (PEMDAS), starting with parentheses and ending with addition/subtraction. The rules for simplifying expressions with exponents include adding and subtracting exponents with the same base, multiplying exponents when raising a power to a power, and the special cases of any number raised to the power of 0 or 1. Negative exponents can be rewritten as fractions and expressions with variables in the exponents can be simplified using the same rules as numerical exponents, while keeping variables and numerical coefficients separate and combining like terms.
  • #1
tmt1
234
0
I have this expression

$$\frac {1} { e^x + \frac {1} {e^x}}$$

and it simplifies to

$$\frac {e^x} { e^{2x} + 1}$$

And I'm not sure how to get this simplification or what rules to apply to get to this simplification.
 
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  • #2
Multiply your original expression by:

\(\displaystyle 1=\frac{e^x}{e^x}\)
 

FAQ: Simplifying an expression with exponents

What is an expression with exponents?

An expression with exponents is a mathematical statement that includes variables, numbers, and exponents. Exponents are used to represent repeated multiplication of a number by itself.

How do you simplify an expression with exponents?

To simplify an expression with exponents, you can follow the order of operations, which is PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction). Start by simplifying any expressions within parentheses, then evaluate any exponents, and finally perform any remaining multiplication, division, addition, and subtraction in that order.

What are the rules for simplifying expressions with exponents?

The rules for simplifying expressions with exponents are:

  • When multiplying two exponential expressions with the same base, add the exponents.
  • When dividing two exponential expressions with the same base, subtract the exponents.
  • When raising a power to a power, multiply the exponents.
  • Any number raised to the power of 0 equals 1.
  • Any number raised to the power of 1 equals itself.
  • Negative exponents can be rewritten as fractions with a positive exponent in the denominator.

Can you simplify expressions with negative exponents?

Yes, expressions with negative exponents can be simplified by rewriting them as fractions with positive exponents. For example, x-2 can be rewritten as 1/x2.

Can you simplify expressions with variables in the exponents?

Yes, expressions with variables in the exponents can be simplified by using the same rules as expressions with numerical exponents. Just be sure to keep the variables separate from any numerical coefficients and combine like terms when possible.

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