Question

If possible, simplify the expression. If the expression cannot be simplified, retype the expression.

5
15
(;) * · (;)" =

Answer 1

`\left((x)/(y)\right)^(-5) \cdot \left((x)/(y)\right)^(15)=\boxed{\left((x)/(y)\right)^(10)}`

Step-by-step explanation:

Given expression:

`\left((x)/(y)\right)^(-5) \cdot \left((x)/(y)\right)^(15)`

To simplify the given expression we can apply exponent laws.

`\boxed{\begin{array}{rl}\underline{\sf Laws\;of\;Exponents}\\\\\sf Product:&a^m * a^n=a^(m+n)\\\\\sf Power\;of\;a\;Quotient:&\left((a)/(b)\right)^m=(a^m)/(b^m)\\\\\end{array}}`

Begin by applying the power of a quotient rule of exponents:

`(x^(-5))/(y^(-5)) \cdot (x^(15))/(y^(15))`

`\textsf{Next, apply the fraction rule:} \quad (a)/(c)\cdot(b)/(d)=(ab)/(cd)`

`(x^(-5)\cdot x^(15))/(y^(-5)\cdot y^(15))`

Now, apply the product rule of exponents:

`(x^(-5+15))/(y^(-5+15))\\\\\\(x^(10))/(y^(10))`

Finally, apply the power of a quotient rule of exponents again:

`\left((x)/(y)\right)^(10)`

Therefore, the simplified expression is:

`\left((x)/(y)\right)^(-5) \cdot \left((x)/(y)\right)^(15)=\boxed{\left((x)/(y)\right)^(10)}`

Answer 2

The original expression is unclear due to typographical errors. In general, simplification involves combining like terms and using properties of exponents, with the goal of removing unnecessary terms and getting the most straightforward expression possible.

Step-by-step explanation:

The expression presented seems to contain typographical errors, making it unclear. Normally, when simplifying an expression in mathematics, we eliminate terms wherever possible to simplify the algebra. For example, if we have an expression such as (53) · (5-2) we can simplify it by subtracting the exponents because of the same base (5), resulting in 53-2 = 51. According to the rule mentioned, we do not write the subscript if it is one, simplifying it further to just 5.

In the given question, the use of the simplified subscript in the final formula cannot be demonstrated as the initial expression is unclear. However, the approach would involve similar steps of combining like terms, simplifying using the properties of exponents, and eliminating unnecessary terms to make the expression as simple as possible. After simplification, always check the answer to see if it is reasonable and error-free.