Chapter 6.8, Problem 6SGR

To determine

Whether the statement “The expression containing powers means to rewrite the expression without parentheses or negative exponents is $\text{simplification }$ ”is true or false.

Answer to Problem 6SGR

The statement “The expression containing powers means to rewrite the expression without parentheses or negative exponents is $\text{simplification }$ ”is true.

Explanation of Solution

Given information:

The statement “The expression containing powers means to rewrite the expression without parentheses or negative exponents is $\text{simplification }$ ”

Consider the provided statement “The expression containing powers means to rewrite the expression without parentheses or negative exponents is $\text{simplification }$ ”

The statement is true because A negative exponent has real numbers $a,b$ and the integers $m,n$ then, its easy to solve the or simplify the negative exponents.

For example: Consider a equation as:

  $y^{-6}\cdot y^4$ .

The bases are same so add the exponents by using the property as:

  $\begin{array}{c}{a}^2\cdot a^4=a^{2+4}=a^6\\ a^{-2}=\frac{1}{a^2}\end{array}$

Now apply the identity to solve the expression as: $a^2\cdot a^4=a^{2+4}=a^6$ .

  $\begin{array}{c}{y}^{-6}\cdot y^4=y^{-6+4}\\ =y^{-2}\end{array}$

Now apply the identity: $a^{-2}=\frac{1}{a^2}$ .

  $\begin{array}{l}{a}^{-2}=\frac{1}{a^2}\\ y^{-2}=\frac{1}{y^2}\end{array}$

This is the way to simplify the negative exponents.

Thus, the statement “The expression containing powers means to rewrite the expression without parentheses or negative exponents is $\text{simplification }$ ” is true.