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-

Question

asked May 27, 2022 112k views

1 Answer

Jeff Lee · Answer 1 · 2022-06-01T20:25:52+0000

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