Answer:
1. Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: [tex]\mathbf{5^3a^2b^4c}[/tex]
5. [tex]x^-6 = \frac{1}{x^6}[/tex]
6. [tex]5^{-3}.3^{-1}=\frac{1}{5^3.3^1}[/tex]
7. [tex]a^{-3}b^0c^4=\frac{c^4}{a^3}[/tex]
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: [tex]=5^{1+1+1}=5^3[/tex]
a.a as [tex]a^{1+1}=a^2[/tex]
b.b.b.b as: [tex]b^{1+1+1+1}=b^4[/tex]
So, our result will be:
[tex]5^3a^2b^4c[/tex]
Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: [tex]\mathbf{5^3a^2b^4c}[/tex]
Question:
Rewrite using positive exponent:
The rule used here will be: [tex]a^{-1}=\frac{1}{a^1}[/tex] 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) [tex]x^{-6} = \frac{1}{x^6}[/tex]
6) [tex]5^{-3}.3^{-1}=\frac{1}{5^3.3^1}[/tex]
7) [tex]a^{-3}b^0c^4=\frac{b^0c^4}{a^3}[/tex]
We know that [tex]b^0=1[/tex] so, we get
[tex]a^{-3}b^0c^4=\frac{b^0c^4}{a^3}=\frac{c^4}{a^3}[/tex]
