Question

Which expressions are equivalent to this exponential expression

A)1/5
B)-2
C)5-^1
D) 5^1

Answer 1

`(5^4* 5^(-2))/(5^3)=(1)/(5)`

A is correct.

Explanation:

Given:
`(5^4* 5^(-2))/(5^3)`

We are given a exponential expression and to simplify it.

Exponent Law:

• Product Rule:
  `a^m* a^n=a^(m+n)`
• Quotient Rule:
  `a^m/ a^n=a^(m-n)`
• Negative Exponent:
  `a^(-m)=(1)/(a^m)`

`\Rightarrow (5^4* 5^(-2))/(5^3)`

Using Quotient rule

`\Rightarrow 5^(4-3)* 5^(-2)`

`\Rightarrow 5^(1)* 5^(-2)`

Using Product Rule

`\Rightarrow 5^(1-2)`

`\Rightarrow 5^(-1)`

Using Negative exponent law

`\Rightarrow (1)/(5)`

Therefore,
`(5^4* 5^(-2))/(5^3)=(1)/(5)`