Evaluate expressions?

Question

Could anyone help explain the process to answer the following step by step pls.

(0.49*10^-6)^-1/2

AND

(1/25)^(-3/2)

Answer 1

Your first step is to eliminate all negative exponents. Remember that when I say eliminate, I don't really mean eliminate; I mean to change it into a positive exponent, by putting it as a numerator.

x^(-3) is the same as 1/(x^3), and 4/(x^(-4)) is the same as 4x^4. The key thing to know is that whenever you move an exponent across the dividing line of the division, its exponent changes sign. Thus, we have:

( 0.49 * 10^(-6) )^(-1/2)

First, let's deal with the outer exponent, and put it as "one over everything to the positive one half"

1 / [ 0.49 * 10^(-6) ]^(1/2)

Now, let's deal with the inner exponent, which is also a negative exponent.

1/ [0.49 * [1/(10^6)] ]^(1/2)

And let's merge the two numbers together into a single fraction.

1/ [0.49/(10^6)]^(1/2)

One thing we're allowed to do is, whenever we have a fraction to an exponent, we're allowed to individually take numerator and denominator to the power of that exponent.

1/ { [0.49]^(1/2) } / [10^6]^(1/2) }

And now, this is the case where we have a complex fraction (i.e. a fraction within a fraction). In order to fix this, we have to multiply numerator and denominator of the big fraction by
[10^6]^(1/2). This effectively brings the denominator of the little fraction to the top, giving us:

{ [10^6]^(1/2) } / { [0.49]^(1/2) }

Remember that whenever you have a power to a power (in this case, we have 10 to the power of 6, to the power of 1/2), we multiply the exponents. 6 times 1/2 is equal to 3.

{ [10^3] } / { [0.49]^(1/2) }

Remember that x^(1/2) is the same as the square root of x. It turns out 0.49 is a square number, and its square root is 0.7, therefore:

[10^3]/[0.7]

Now, it's a matter of simplification. 10^3 = 1000

1000/0.7

Which we can plug directly into our calculator, or, if you wish, you can turn this into a fraction of whole numbers by multiplying top and bottom by 10.

10000/7

This can't be a reduced but it's still the final answer.

Answer 2

Ok first (0.49 * 10^-6)^-1/2 is the same as

1/(0.49 * 10^-6)^1/2 in general x^-y =(1/x)^y

=1 428.57143

(1/25)^-3/2= 25^3/2

25^1/2=SQRT(25)=5 so we need 5^3=125

Answer 3

(0.49*10^-6)^-1/2
= 1 / (0.49*10^-6)^1/2 (negative exponent = inverse)
= 1 / [0.49^1/2 * (10^-6)^1/2] (distribute the exponent 1/2)
= 1 / (0.7 * 10^-3) (0.7² = 0.49 and multiply the exponents of 10)
= 1000 / 0.7
= 10000 / 7
= 1428 and 5/7

(1/25)^(-3/2)
= (5^-2)^(-3/2)
= 5^(-2 * -3/2)
= 5^3
=125

Answer 4

1. (A*B)^C = A^C * B^C
A = 0.49
B = 10^-6
0.49 ^ -1/2 = 1 / ( 0.49 ^ 1/2 ) = 1 / 0.7 = 10/7 = 1.428571...
10^-6 ^ -1/2 = 10 ^ 3
1.428 * 10 ^3 = 1428.571...

2. A^(B*C) = (A^B)^C
A = 1/25
B = -1/2
C = 3
(1/25 ^ -1/2) = ( 25 ^ 1/2 ) = 5
5 ^ 3 = 125

Answer 5

(0.49*10^-6)^-1/2
= (0.49/10^6)^-.5
=1/(.49/10^6)^.5
=1/(.7/10^3)
=1/.0007
=1428.5714

(1/25)^(-3/2)
= 1/(1/25)^3/2
=1/(1/125)
=125

Answer 6

-9x-3x-3=-80 one that is somewhat straightforward parenthesis mean that expression or numbers flow first and multiply if there are no longer any different symbols, although pondering they are all in parenthesis that's implying which you would be able to desire to multiply all of them jointly in no specific order. 2LT.

Answer 7

1]
[.49*10^-6]^-1/2
=.49^-1/2*10^-3
=[1/.7]/1000
=1/.0007
=1428.571
2][1/25]^-3/2
=[25^-1]-3/2
=25^3/2
=5^3
=125