Question

Question 5 Multiple Choice Worth 4 points)
Which expression is equivalent to (5^3)-^2?

1/5^3

-1/5.5.5.5.5.5

5^3

1/5.5.5.5-5.5

Answer 1

Answer:

$\large\boxed{\dfrac{1}{5\cdot5\cdot5\cdot5\cdot5\cdot5}}$

Step-by-step explanation:

$\text{Use}\ (a^n)^m=a^{nm}\\\\(5^3)^{-2}=5^{(3)(-2)}=5^{-6}\\\\\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{5^6}\\\\\text{use}\ a^n=\underbrace{a\cdot a\cdot a\cdot ...\cdot a}_{n}\\\\=\dfrac{1}{5\cdot5\cdot5\cdot5\cdot5\cdot5}$