afraaalatiki
Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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 :

absor201

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 hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.