Question

Diagnostic: Algebra (solve without using a calculator)

Answer 1

\[a.(-3)^4\]
\[b. -3^4\]
\[c. 3^{-4}\]
\[d. \frac{ 5^{23} }{ 5^{21} }\]
\[e.\left( \frac{ 2 }{ 3 } \right)^{-2}\]
\[f.16^{\frac{ 3 }{ 4 }}\]

Answer 2

A. is 81

Answer 3

okay! how did you get 81?

Answer 4

b is -27

Answer 5

okay! how did you get -27?

Answer 6

a.) 81
b.)81
c.)1/81
d.)1^2
e.)9/4

Answer 7

oh wait yeah b is 81

Answer 8

whoooaaa we got a mathematician :) thanks @FriedRice you seem like a cool person :)

Answer 9

if you have a calculator you can do all this..Lulzz.

Answer 10

f.) 8

Answer 11

its not that easy for me also im trying my best @nincompoop

Answer 12

@uri I can't use calculaturz :(

Answer 13

you can use google calculator. :3

Answer 14

I allow youu.

Answer 15

I need step-by-step solution @FriedRice can you help?

Answer 16

sure but from what letter?

Answer 17

all please :)

Answer 18

I like friedrice with soysauce by the way!

Answer 19

@nincompoop, you don't need any help with this.

Answer 20

\((-3)^4 = (-3)(-3)(-3)(-3) = (3)(3)(3)(3) = 9 \times 9\)

Answer 21

\(-3^4 = -(3)(3)(3)(3) = -(9)(9) = -9 \times 9\)

Answer 22

a.(−3)^ 4 = -3 *-3 * -3 * -3 = 81

b.−3^ 4 = -3 * -3 * -3 * -3 = 81

c.3 ^−4 = 1/3^4 = 1/81

d.5 ^23 / 5 ^ 21 = simplify 1^2

e.(2 / 3 ) ^ −2 =distribute 2^-2/3^-2 3^2 / 2^2 = 9 / 4

f.16 ^ 3 / 4 = 16 raised to the 3/4 power means that you should raised 16 to the 3rd power first,that gives you 16x16x16=4096,then you take the 4th root of 4096 to find the answer. IT means that you want to find the # that multiplies itself 4 times that gives you 4096, which is 8 here.

Answer 23

\[3^{-4} = \frac{1}{3^4} = \frac{1}{(3^2)(3^2)} = \frac{1}{9 \times 9}\]

Answer 24

Negative exponent means "multiplicative inverse"

Answer 25

\[\frac{5^{23}}{5^{21}} = 5^{23 - 21} = 5^2\]

Answer 26

I need to prove answers, what does that mean?

Answer 27

The general rule is this:

\[\frac{a^b}{a^c} = a^{b-c}\]

Answer 28

\[a^{-b} = \frac{1}{a^b}\]

Answer 29

\[a^{\frac{b}{c}} = \sqrt[c]{a^b}\]

Answer 30

\[16^{\frac{3}{4}} = \sqrt[4]{16^3}=\sqrt[4]{(2^4)^{3}} = \sqrt[4]{(2^3)^4} = 2^3\]

Answer 31

The general rule for that trick is
\[(a^b)^c = (a^c)^b\]

Answer 32

associative property in exponents ?

Answer 33

I guess you could think of it that way, but it's not really associative property.

Answer 34

I couldn't think of any wording :X

Answer 35

Well, I hope that helped. Good luck bro.