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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-example-1

1 Answer

14 votes

Answer:

1)
((-2)^(-5))/((-2)^(-10))=-32

2)
2^(-1).2^(-4) = (1)/(32)

3)
(-(1)/(2) )^3.(-(1)/(2) )^2=-(1)/(32)

4)
(2)/(2^(-4)) = 32

Explanation:

1)
((-2)^(-5))/((-2)^(-10))

Solving using exponent rule:
a^(-m)=(1)/(a^m)


((-2)^(-5))/((-2)^(-10))\\=(-2)^(-5+10)\\=(-2)^(5)\\=-32

So,
((-2)^(-5))/((-2)^(-10))=-32

2)
2^(-1).2^(-4)

Using the exponent rule:
a^m.a^n=a^(m+n)

We have:


2^(-1).2^(-4)\\=2^(-1-4)\\=2^(-5)

We also know that:
a^(-m)=(1)/(a^m)

Using this rule:


2^(-5)\\=(1)/(2^5)\\=(1)/(32)

So,
2^(-1).2^(-4) = (1)/(32)

3)
(-(1)/(2) )^3.(-(1)/(2) )^2

Solving:


(-(1)/(2) )^3.(-(1)/(2) )^2\\=(-(1)/(8) ).((1)/(4) )\\=-(1)/(32)

So,
(-(1)/(2) )^3.(-(1)/(2) )^2=-(1)/(32)

4)
(2)/(2^(-4))

We know that:
a^(-m)=(1)/(a^m)


(2)/(2^(-4))\\=2* 2^4\\=2(16)\\=32

So,
(2)/(2^(-4)) = 32

User Jeff Lee
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