Rewrite the expression using only positive exponents and simplify.?

Question

(10x)^0 / (4x ^ -2) ^ (3/2)

I am doing this so I have an idea as to what I am doing for the rest of my summer homework.

Answer 1

On top, any nonzero raised to the zero power = 1. This means there is an excluded value to your problem: x ≠ 0. (This would give you the math no-no of 0^0 in your original expression.)

On bottom, you have (4 • x^-2)^(3/2), which is
4^(3/2) • (x^-2)^(3/2)

4^(3/2) = √(4³) = √64 = 8. [Remember that with rational (a fraction for your) exponents, the top number is a power and the bottom number is a root.]

(x^-2)^(3/2) = x^(-3). [Remember that when taking a power of a power, you multiply the exponents. (-2)(3 / 2) = -3.]

The denominator of a fraction cannot be zero, either, so there's one more excluded value to consider: x ≠ 0. Thankfully, it's the same as the top one.

Now, you've got 1 / [8 • x^(-3)]. The term with the negative exponent in the bottom will flip to the top, giving you a final simplification of

x³ / 8,
or (1 / 8)x³, as long as x ≠ 0.

Answer 2

(10x)^0 = 1
(4x^-2)^(3/2) = (4)^(3/2) (x^-2)^(3/2)
4^(3/2) = (sqrt(4))^3 = 2^3 = 8
(x^-2)^(3/2) = x^(-2*3/2) = x^-3
So (4x^-2)^(3/2) = 8x^-3
Therefore,
(10x)^0 / (4x ^ -2) ^ (3/2)
= 1/(8x^-3)
Move x^-3 to the numerator to make the exponent positive.
= x^3/8 or (x^3)/8

Answer 3

(10x)^0 = 1
(4x^-2)^(3/2) = (4x^-3) = 1/ (64 x^3)

so 1/ (1/ 64 x^3) = 64 x^3

Answer 4

(10x)^0 = 1
(4x^-2)^3/2 = 4^3/2 x^-3
so it is
x^3/8

Answer 5

(10x)^0 = 1
(4x^-2)^(3/2) = 4^(3/2) = 8x^(-3) = 8/(x^3)

1/(8/(x^3))
(1/1)/(8/x^3)
(1/1)*((x^3)/8)

ANS : (x^3)/8

Answer 6

Using Answers to cheat on homework?

Answer 7

(x/4)^(3/2)

Answer 8

64x^3