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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]

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