Which expressions are in their simplest form? Check all that apply.
$\frac{1}{3}+x^7$
$x^{-9}-\frac{1}{y}$
$\frac{1}{x^3}-\frac{1}{y^4}$
$x^3+\frac{1}{y}-t^6$
$x^{-5}-y^{-4}$
Answer (1)
Check if the terms in each expression can be combined or simplified.
3 1 + x 7 is in simplest form.
x − 9 − y 1 is in simplest form.
x 3 1 − y 4 1 is in simplest form.
x 3 + y 1 − t 6 is in simplest form.
x − 5 − y − 4 is in simplest form.
All expressions are in their simplest form: $\boxed{\text{All expressions}}
Explanation
Understanding the Problem We need to determine which of the given expressions are in their simplest form. An expression is in simplest form if it cannot be simplified further by combining like terms or performing other algebraic operations.
Analyzing Each Expression
3 1 + x 7 : This expression is already in its simplest form because the terms are not like terms and cannot be combined.
x − 9 − y 1 : This can be rewritten as x 9 1 − y 1 . This expression is in simplest form because the terms cannot be combined.
x 3 1 − y 4 1 : This expression is in simplest form because the terms cannot be combined.
x 3 + y 1 − t 6 : This expression is in simplest form because the terms cannot be combined.
x − 5 − y − 4 : This can be rewritten as x 5 1 − y 4 1 . This expression is in simplest form because the terms cannot be combined.
Conclusion Therefore, all the expressions are in their simplest form.
Examples
Simplifying expressions is like organizing your room. You group similar items together to make it easier to find things. In math, it helps in solving equations and understanding relationships between variables. For example, if you are calculating the total cost of items with different discounts, simplifying the expression first can make the calculation easier and more accurate. This skill is useful in everyday situations like budgeting, cooking, and home improvement projects.
