Write each expression with positive exponents only and then simplify:?

Question

a. 2 ^–1 + 4^ –1
b. ( 2/5 )^ -3

Can someone please explain?

Answer 1

a. 2^-1 + 4^-1

2^-1 = 1/2^1 = 1/2
4^-1 = 1/4^1 = 1/4

1/2 + 1/4 = 2/4 + 1/4 = 3/4

b. ( 2/5 )^ -3

(2/5)^-3 = 1 / (2/5)^3 = (5/2)^3 = 125/8

Answer 2

When you have negative exponents, it simply means you move from the numerator or denominator to the opposite. So in a.) 2 ^–1 + 4^ –1 becomes (1/2^1)+(1/4^1) which simplifies to (1/2) + (1/4). Adding these equals (3/4).

b.) ( 2/5 )^ -3 is equal to (1) / (2/5)^3. This equals (1) / (8/125). This can be simplified to 125/8.

Hope this helps!

Answer 3

When a number is put to the power of a negative exponent, it means take the inverse of the number and put it to a positive exponent. Therefore, 2^-1 really means 1/(2^1). This equals 1/2.

Now 4^-1 is actually 1/(4^1). So this equals 1/4
Now 1/2 +1/4 = 3/4

b) Do the same thing. The inverse of 2/5 is 5/2 So take this and put it to the power of +3. (5/2)^3 is 125/8.

Answer 4

1/2^1 + 1/4^1= 2/4 + 1/4= 3/4

5/2^3= 125/8

Answer 5

-ve power means the reciprocal needs to be written

a. 1/2 + 1/4
= 6/8 = 3/4

b. (5/2)^3
= 125/8

Answer 6

ok
a negative exponent means to invert the number before taking it to the designated power.
so:
a. 2 ^–1 + 4^ –1 = 1/2 + 1/4 = 3/4
and,
b. ( 2/5 )^ -3 = (5/2)^3 = 125/8

Answer 7

2^(-1) + 4(-1) = should be multiplication, not additiion
2^(-1) * ((2)^2)^-1)
2^(-1) * 2^(-2) = 2(-3) = 1/2^3 = 1/8 [2^(-3)]= 1/[2^(3)]

(2/5)^(-3) = 2^(-3) / 5^(-3)
= 5^(3) / 2^(3)

Answer 8

2^-1 + 4^-1
(1/2)^1 + (1/4)^1
1/2 + 1/4
3/4

(2/5)^-3
(5/2)^3
125/8