what does it mean when it says write the expressions as an exponent with a base of _ ?

Question

for example it says:

Write the expression with the base 3:
a. 3 to the power of 2 times 3 to the power of 5

OR

Write 2 to the power of 60 as an exponent with the base of:
a. 4 [ the answer is 4 to the power of 30. WHY? & HOW?]

Answer 1

3 is the base...

3^2 x 3^5

2^(60) is the same as 4^(30)

since 4 is double the base 2... you will only have to raise 4 to half the power that 2 was raised to...

Why? Because you need to multiply MORE 2's to get the same number as you would mulitplying 4's

and vice versa... you need to multiply LESS 4's to get the same number as you would multiplying 2's


Take for example the number 16...

16 can either be written in exponential form as 4^2 or 2^4

16 = 4 x 4
16 = 2 x 2 x 2 x 2

you need to multiply more 2's than 4's.... since 4 is "double" the base of 2... you need half as many 4's as two.... you need only muliply two 4's.... but since 2 is half of 4, you have to raise it to double the power that 4 was raised to...

Answer 2

The base is the the number and the power is the exponent!
For eg. in 2^5, 2 is the base while 5 is the exponent!
2 to the power 60 can also be written as 2^30*2= 4^30.

Answer 3

I'm assuming you know that the "base" number is the big number on the line and the "exponent" is the number superscripted....

assuming that and using ^ to indicate an exponent so I don't have to try to format this page,
3^2 * 3^5 = is the question you asked.
The law of exponents says when you multiply numbers with exponents you find the answer by adding the exponents

so 2+5=7
3^2 * 3^5 = 3^7 expanded into numbers
9*243=2187

2^2= 4
so 2^60 = (2^2)30
When you raise an exponential equation to a power you multiply the exponents so 2*30 = 60
again 2^2 = 4 ===>
2^60 = 4^30
that's why as clearly as I can explain it here.

Answer 4

The base is the number being raised to that power. i.e. 3^5 has a base of 3 and an exponent of 5. When they say rewrite 2^60 into a base 4 expression, they want you to find 4^x, where x is given by 4^x = 2^60. Basically, just solve that for x.

Answer 5

Ok well part A. is simple. (^ means raised to the _ power)

a. 3^2 x 3^5
so when you multiply numbers with exponents, you simply add the exponents together, so the answer is 3^7

the next one is a little tricky. 2^60 becomes 4^30 why?

well when you have to change the base, you have to change the exponent. you know that 2^60 = 4^x. They have to be equal. So roughly, 2^60 = 1.15 x 10^18. THerefore, 4^x = 1.15 x 10^18, when you solve for x, it is 30.

Answer 6

The base is the big number and the exponent is the small number that goes up and to the right.

a. 3^2(3^5)
Then you solve. 9(243) = 2187

The second is saying to change 2^60 to 4 to the power of something.

Look at it like this:
2^60 = 4^x

4 can be written as a base of 2 ---> 2^2

2^60 = 2^2x

When the bases are equal, the exponents are too.
60 = 2x
x = 30

2^60 = 4^30

Answer 7

firsst is 3 to the power of 7, because :
3x3 is 3 to the power of 2
3x3x3x3x3 is 3 to the power of 5
if u multiply both expresion yould have
3x3x3x3x3x3x3 that is 3 to the power of 7
use the same logic for the next question
imagine 2 to th epower of 60, u will have 60 2s
if u want to use 4 as a base, for a two 2s u will put one 4, so, it would be 4 to the power of (60 divided by 2)
i hope it helped

Answer 8

it means put it all together with a base of 3 such as.
(3^2)*(3^5)=3^7

2^60 is the same as (2^2)^30 because when you mutiply two terms the exponents add together if they have the same base, but in order to mutiply exponents you have to take you exponential term and put it to another exponenet. so 2^2 becomes 4 and it ends up 4^30

feel free to email me btw if you still don't understand

Answer 9

a^m * a^n = a^(m+n)
So 3^2 * 3^5 = 3 ^(2+5) = 3^7

(2^m)^n = 2^(m*n)
So, 2^60 = (2^2)^30
4^30

Answer 10

it means expressing the given number as a raise to the power b
where a is base and b is exponent