If the square of A-B is known to the power of-27 to the power of 2B, the power of a to the power of 5b is equal to the power of a to the power of 5B

(-8^a)^2/4^(5-2b)
=2^(6a)/2^(10-4b)
=2^(6a-10+4b)
=2^(2-2b)
6a-10+4b=2-2b
a+b=2
(9^a)^b=3^(2ab)=(3^b)^a/27=3^(ab-3)
2ab=ab-3
ab=-3
a^2+b^2=(a+b)^2-2ab=4+6=10

Given that the a power of 10 = 200, the B power of 10 = 1 / 5, find the value of the a power of 4 divided by the 2B power of 2 Do you know how they can get the value of a to the power of 2 B by the power of 2 B? I don't understand~

10^a=200,10^b=1/5
a=lg200=2+lg2,
b=lg(1/5)=lg2-1
a-b=2+lg2-lg2+1=3
4^a/2^(2b)
=2^(2a)/2^(2b)
=2^(2a-2b)
=2^6
=64

If the a power of 10 is equal to 20, and the B power of 10 is equal to the negative first power of 5, find the value of the a power of 9 divided by the 2B power of 3

A:
10A = 20, 10b = 1 / 5, so 10A / 10B = 10 (a-b) = 100 = 102,
a-b=2,
9a/32b=3(2a-2b)=81

What's the second power of X? What's the minus half power

Half power of x = √ x
The negative half power of x = 1 / √ x
The two are reciprocal

What is the second power of minus 4 equal to one?

=（-1/4）2=1/16
If my answer can solve your problem, if you have any questions, I would like to thank you for your support

How much is 2 to the power of 2? How much to the power of such a few

(2 / 3) to the power of 2000 times (1.5) to the power of 1999 times (- 1) to the power of 1999?

（2/3）^2000x1.5^1999x(-1)^1999
=2/3x(2/3x1.5)^1999x(-1)^1999
=2/3x(-1)
=-2/3

3 times 4 to the power of 1 x and 6 to the power of 1 x equals 2 times 9 to the power of 1

Divide both sides by 9 ^ (1 / x)
3*(4/9)^(1/x)+(6/9)^(1/x)=2
3*(4/9)^(1/x)+(2/3)^(1/x)=2
Let a = (2 / 3) ^ (1 / x)
Then 3A 2 + A-2 = 0
(a+1)(3a-2)=0
Obviously, a > 0
So a = (2 / 3) ^ (1 / x) = 2 / 3
1/x=1
X=1

1 / 2 to the power of x equals 1 / 2 times 1 / 4 times 1 / 8 times 1 / 16 times 1 / 32 times 1 / 64 to find the value of X

Because it is equal to 6, there is no 5, so y = Z, 6 we can see that it is 2 * 3. If you take 8 to the third power of 2, 9 to the square of 3, 16 to the fourth power of 2, plus y = Z, we can get 5y-3x = 1,2x-3y

If the x power of 2 is equal to 3 and the Y power of 2 is equal to 5, find the 2x-y power of 4

The 2x-y power of 4
It's four to the 2x power divided by four to the Y power
2 to the x power is 3
The 2x power of 4 is the 4x power of 2, and the x power of 2 is the fourth power,
The fourth power of 3 is 81
The Y power of 4 is the 2Y power of 2
The Y power of 2 is equal to 5
2 to the 2Y power of 2 is 25
81/25

If the square of A-B is known to the power of-27 to the power of 2B, the power of a to the power of 5b is equal to the power of a to the power of 5B