Afraaalatikiidn
Answered

Join IDNLearn.com and start getting the answers you've been searching for. Find the answers you need quickly and accurately with help from our knowledgeable and experienced experts.

Use the rules of exponents to simplify the expressions. Match the expression with its equivalent value.
(-2)
1.
1-21-10
32
2. 21.24
-32
3.
32
1
4.
2-

Use The Rules Of Exponents To Simplify The Expressions Match The Expression With Its Equivalent Value 2 1 12110 32 2 2124 32 3 32 1 4 2 class=

Sagot :

Absor201idn

Answer:

1) [tex]\frac{(-2)^{-5}}{(-2)^{-10}}=-32[/tex]

2) [tex]2^{-1}.2^{-4} = \frac{1}{32}[/tex]

3) [tex](-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}[/tex]

4) [tex]\frac{2}{2^{-4}} = 32[/tex]

Step-by-step explanation:

1) [tex]\frac{(-2)^{-5}}{(-2)^{-10}}[/tex]

Solving using exponent rule: [tex]a^{-m}=\frac{1}{a^m}[/tex]

[tex]\frac{(-2)^{-5}}{(-2)^{-10}}\\=(-2)^{-5+10}\\=(-2)^{5}\\=-32[/tex]

So, [tex]\frac{(-2)^{-5}}{(-2)^{-10}}=-32[/tex]

2) [tex]2^{-1}.2^{-4}[/tex]

Using the exponent rule: [tex]a^m.a^n=a^{m+n}[/tex]

We have:

[tex]2^{-1}.2^{-4}\\=2^{-1-4}\\=2^{-5}[/tex]

We also know that: [tex]a^{-m}=\frac{1}{a^m}[/tex]

Using this rule:

[tex]2^{-5}\\=\frac{1}{2^5}\\=\frac{1}{32}[/tex]

So, [tex]2^{-1}.2^{-4} = \frac{1}{32}[/tex]

3) [tex](-\frac{1}{2} )^3.(-\frac{1}{2} )^2[/tex]

Solving:

[tex](-\frac{1}{2} )^3.(-\frac{1}{2} )^2\\=(-\frac{1}{8} ).(\frac{1}{4} )\\=-\frac{1}{32}[/tex]

So, [tex](-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}[/tex]

4) [tex]\frac{2}{2^{-4}}[/tex]

We know that: [tex]a^{-m}=\frac{1}{a^m}[/tex]

[tex]\frac{2}{2^{-4}}\\=2\times 2^4\\=2(16)\\=32[/tex]

So, [tex]\frac{2}{2^{-4}} = 32[/tex]

We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.