Question

Simplify the following expression.

4^6 ÷ 4-^2
A. 4^4
B. 4^-8
C. 4^8
D. 4^-12


6. Kelly works at her own nail salon. Today, she did 13 manicures and received $71.50 overall in tips.

If x represents the cost of each manicure, which of the following equations can be used to find the total amount of money she earned, including tips, for her nail salon today?
A. y = 71.5(x + 13)
B. y = 13x + 71.5
C. y = 13(x + 71.5)
D. y = 71.5x + 13

Answer 1

http://www.math-play.com/image-exponents-rules.jpg <--- use the 1st rule listed there

for 6) well, let's see, tips were $71.50 flat, regardless of how many manicures she did
she charges "x" for each manicure
she happens to have done 13 today
let's take a peek at a few prices for her manicure
\(\large y=
\begin{array}{ccllll}
price&quantity&tips\\
\hline\\
\$2&13&17.50\implies 13(2)+17.50\\
\$5&13&17.50\implies 13(5)+17.50\\
\$9&13&17.50\implies 13(9)+17.50\\
\$13&13&17.50\implies 13(13)+17.50\\
\$17&13&17.50\implies 13(17)+17.50\\
\end{array}\)

any ideas?

Answer 2

hmmm should be 71.50 I'm kinda shortchanging here =) so \(\large y=
\begin{array}{ccllll}
price&quantity&tips\\
\hline\\
\$2&13&71.50\implies 13(2)+71.50\\
\$5&13&71.50\implies 13(5)+71.50\\
\$9&13&71.50\implies 13(9)+71.50\\
\$13&13&71.50\implies 13(13)+71.50\\
\$17&13&71.50\implies 13(17)+71.50\\

\end{array}\)

Answer 3

71.50 is the tips and is the constant because it is given to you
number of manicures(13) times x is how much money she earned from manicures you can add both of them up to get the total y
so you get
y=13x+71.50

Answer 4

the first question is just simply knowing your exponent rules

Answer 5

\[\frac{4^{6} }{ 4^{-2} }\]

Answer 6

when dividing exponents just subtract them
6-(-2)=8 so
the answer is 4^8