Question

Select all the correct answers.
Which expressions are equivalent to this exponential expression?

Answer 1

Answer:

$5^2 \text{ or } 25$

Step-by-step explanation:

We can use exponent rules to simplify the expression:

$\displaystyle \dfrac{(5^2)^{-3}\cdot 5^4}{5^{-4}}$

First, we can simplify the power to a power term with the rule:

• $(x^a)^b = x^{ab}$

   ↓↓↓

$\displaystyle \dfrac{5^{2(-3)}\cdot 5^4}{5^{-4}}$

$= \displaystyle \dfrac{5^{-6}\cdot 5^4}{5^{-4}}$

Next, we can combine the terms on the top using the multiplication of base rule:

• $x^a\cdot x^b=x^{(a+b)}$

   ↓↓↓

$\displaystyle \dfrac{5^{(-6 + 4)}}{5^{-4}}$

$= \dfrac{5^{-2}}{5^{-4}}$

Finally, we can use the quotient of base rule:

• $\dfrac{x^a}{x^b} = x^{(a-b)}$

   ↓↓↓

$5^{(-2-(-4))}$

$=5^{(-2+4)}$

$\boxed{=5^2 = 25}$