Question

Please answer! I crossed out the ones you don’t have to complete.

Answer 1

Answer:

1. Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: $\mathbf{5^3a^2b^4c}$

5.  $x^-6 = \frac{1}{x^6}$

6. $5^{-3}.3^{-1}=\frac{1}{5^3.3^1}$

7. $a^{-3}b^0c^4=\frac{c^4}{a^3}$

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: $=5^{1+1+1}=5^3$

a.a as $a^{1+1}=a^2$

b.b.b.b as: $b^{1+1+1+1}=b^4$

So, our result will be:

$5^3a^2b^4c$

Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: $\mathbf{5^3a^2b^4c}$

Question:

Rewrite using positive exponent:

The rule used here will be: $a^{-1}=\frac{1}{a^1}$ 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) $x^{-6} = \frac{1}{x^6}$

6) $5^{-3}.3^{-1}=\frac{1}{5^3.3^1}$

7) $a^{-3}b^0c^4=\frac{b^0c^4}{a^3}$

We know that $b^0=1$ so, we get

$a^{-3}b^0c^4=\frac{b^0c^4}{a^3}=\frac{c^4}{a^3}$