Question

How do I solve this??? I've tried every method I know. It wants me to simplify.

Answer 1

`\sf 9^(14)* 9^2 / 9^5 = 9^{\boxed{\sf 11} }`

Explanation:

To solve the expression
`\sf 9^(14)* 9^2 / 9^5`, we can use the power of a power property and the power of a quotient property.

Power of a Product Property

The power of a Product Property states that:

`\boxed{\boxed{\sf a^m * a^n = a^((m+ n)) }}`

Power of a Quotient Property

The power of a quotient property states that:

`\boxed{\boxed{ \sf a^m/ a^n = a^((m-n) )}}`

Using these properties, we can simplify the expression as follows:

`\sf 9^(14)* 9^2 / 9^5`

Applying Product Property:

`\sf 9^(14+2) / 9^5`

`\sf 9^(16) / 9^5`

Now

Applying Quotient Property:

`\sf 9^(16-5)`

`\sf 9^(11)`

Therefore,

`\sf 9^(14)* 9^2 / 9^5 = 9^{\boxed{\sf 11} }`

Answer 2

11

Explanation:

Important concepts and formulas:

Laws of exponents

The following laws of exponents are going to help us solve this question

• Product of powers rule :
  `x^m * x^n =x^m^+^n`
• Quotient of powers rule :
  `x^m/ x^n=x^m^-^n`

PEMDAS

PEMDAS is the order of operations we use to solve expressions.

Parenthesis

Exponents

Multiplication and Division (left to right)

Addition and Subtraction (left to right)

This tells us that its important to go from left to right when we have multiplication and division meaning that we start with whatever comes first. Not doing so can lead us to getting the wrong answer

Finding the value

Given expression :
`9^1^4*9^2/9^5`

First we do the multiplication as it comes first
`9^1^4*9^2`

Using the product of powers rule we get
`9^1^4*9^2=9^1^4^+^2=9^1^6`

We are left with
`9^1^6/9^5`

Using the quotient of powers rule we get
`9^1^6/9^5=9^1^6^-^5=9^1^1`

The value that goes inside of the green box is 11