Answer:
24x
Step-by-step explanation:
The product of 24 and a number means that 24 is multiplied by some number. When we use the term "some number" in math, we often use "x" as a representation of that number.
Answer:
1. Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: ![\mathbf{5^3a^2b^4c}](https://tex.z-dn.net/?f=%5Cmathbf%7B5%5E3a%5E2b%5E4c%7D)
5. ![x^-6 = \frac{1}{x^6}](https://tex.z-dn.net/?f=x%5E-6%20%3D%20%5Cfrac%7B1%7D%7Bx%5E6%7D)
6. ![5^{-3}.3^{-1}=\frac{1}{5^3.3^1}](https://tex.z-dn.net/?f=5%5E%7B-3%7D.3%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7B5%5E3.3%5E1%7D)
7. ![a^{-3}b^0c^4=\frac{c^4}{a^3}](https://tex.z-dn.net/?f=a%5E%7B-3%7Db%5E0c%5E4%3D%5Cfrac%7Bc%5E4%7D%7Ba%5E3%7D)
Step-by-step explanation:
Question 1:
We need to rewrite the expression using exponents
5.a.b.b.5.c.a.b.5.b
We will first combine the like terms
5.5.5.a.a.b.b.b.b.c
Now, if we have 5.5.5 we can write it in exponent as: ![=5^{1+1+1}=5^3](https://tex.z-dn.net/?f=%3D5%5E%7B1%2B1%2B1%7D%3D5%5E3)
a.a as
b.b.b.b as: ![b^{1+1+1+1}=b^4](https://tex.z-dn.net/?f=b%5E%7B1%2B1%2B1%2B1%7D%3Db%5E4)
So, our result will be:
![5^3a^2b^4c](https://tex.z-dn.net/?f=5%5E3a%5E2b%5E4c)
Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: ![\mathbf{5^3a^2b^4c}](https://tex.z-dn.net/?f=%5Cmathbf%7B5%5E3a%5E2b%5E4c%7D)
Question:
Rewrite using positive exponent:
The rule used here will be:
which states that if we need to make exponent positive, we will take it to the denominator.
Applying thee above rule for getting the answers:
5)
6) ![5^{-3}.3^{-1}=\frac{1}{5^3.3^1}](https://tex.z-dn.net/?f=5%5E%7B-3%7D.3%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7B5%5E3.3%5E1%7D)
7) ![a^{-3}b^0c^4=\frac{b^0c^4}{a^3}](https://tex.z-dn.net/?f=a%5E%7B-3%7Db%5E0c%5E4%3D%5Cfrac%7Bb%5E0c%5E4%7D%7Ba%5E3%7D)
We know that
so, we get
![a^{-3}b^0c^4=\frac{b^0c^4}{a^3}=\frac{c^4}{a^3}](https://tex.z-dn.net/?f=a%5E%7B-3%7Db%5E0c%5E4%3D%5Cfrac%7Bb%5E0c%5E4%7D%7Ba%5E3%7D%3D%5Cfrac%7Bc%5E4%7D%7Ba%5E3%7D)
I think its a number no idea