Question

List three different ways to write 5^11 as the product of two powers. Explain why all three of your expressions are equal to 5^11

Answer 1

What problem are you having with this one?

Answer 2

idk how to wright this and i don't know how to list two different products and get the same for 5^11

Answer 3

Rules of exponents:
\[x^{m}\cdot x^{n}=x^{n+n}\\
(x^{m})^n=x^{m\cdot n}\]By using these, you can change things around.

Answer 4

idk how to do that i am just getting into this

Answer 5

OK. You know what \(5^{11}\) means? What would be done to 5, right?

Answer 6

yes

Answer 7

Another way of saying 5 is \(5^1\). That works for anything. \(x=^1\). So that gives one solution:

\(5^{11}=5^1\cdot 5^1\cdot 5^1\cdot 5^1\cdot 5^1\cdot 5^1\cdot 5^1\cdot 5^1\cdot 5^1\cdot 5^1\cdot 5^1\)

Answer 8

o

Answer 9

\(x=x^1\) missed an x there.

Answer 10

5^5*5^6

Answer 11

Now, lets take some of those and use the ... yes!

Answer 12

And 6 can be expressed using \((x^{m})^n=x^{m\cdot n}\) as \((5^3)^2\), but I am not sure if they wanted that in this one.

Answer 13

i dont really think so not yet this is a Quiz it might be on the test

Answer 14

So yah, rules of exponents. If you have items of th same base, like the 5, you can just add up the exponents. \(5^{11}=5^a\cdot 5^b\cdots 5^n\) as long as a to n add up to 11.

Answer 15

okay

Answer 16

Why \((5^3)^2\) works as a power rule is not too hard if you think about what the outer power means. Multiply everything in the () by itself. So \((5^3)^2=(5^3)(5^3)=5^{3+3}=5^6\)

Answer 17

So there you go, an overview of a ouple exponent rules. Don't have too much fun!

Answer 18

thank you @e.mccormick

Answer 19

np. Exponents are not too bad, and as you get into them more you will learn how they, roots, and logs are all related.

Answer 20

\[5^{11}=5^{x+y},where x+y=11\]
now you can find the values of x & y satisfying the above eq.