Question

Which expressions are equivalent to this exponential expression

Answer 1

Answer:

$\dfrac{5^4\times 5^{-2}}{5^3}=\dfrac{1}{5}$

A is correct.

Step-by-step explanation:

Given: $\dfrac{5^4\times 5^{-2}}{5^3}$

We are given a exponential expression and to simplify it.

Exponent Law:

• Product Rule: $a^m\times a^n=a^{m+n}$
• Quotient Rule: $a^m\div a^n=a^{m-n}$
• Negative Exponent:  $a^{-m}=\dfrac{1}{a^m}$

$\Rightarrow \dfrac{5^4\times 5^{-2}}{5^3}$

Using Quotient rule

$\Rightarrow 5^{4-3}\times 5^{-2}$

$\Rightarrow 5^{1}\times 5^{-2}$

Using Product Rule

$\Rightarrow 5^{1-2}$

$\Rightarrow 5^{-1}$

Using Negative exponent law

$\Rightarrow \dfrac{1}{5}$

Therefore,  $\dfrac{5^4\times 5^{-2}}{5^3}=\dfrac{1}{5}$