Question

Write two different equivalent forms of the expression 2⁽ˣ⁺³⁾

Answer 1

Two equivalent forms of the expression 2^{(x+3)} are 2^x × 2^3 and (2^x) × 8, utilizing the properties of exponents.

Step-by-step explanation:

The expression 2^{(x+3)} can be represented in different equivalent forms. We can use the properties of exponents to transform this expression into other equivalent expressions.

First Equivalent Form

The first equivalent form uses the property that allows us to multiply exponential terms with the same base by adding their exponents. Therefore, 2^{(x+3)} can be rewritten as 2^x × 2^3. Here we have separated the exponent into two parts, x and 3, and applied the rule of multiplying exponentiated quantities, resulting in the multiplication of two power terms of 2.

Second Equivalent Form

The second equivalent form takes advantage of the distributive property over the exponent. We can write 2^{(x+3)} as (2^x) × (2^3), which simplifies further to (2^x) × 8, as 2^3 equals 8. This form illustrates the squaring of exponentials and how we can simplify the expression by calculating part of the exponent.