Exponents - Error Log

Question 1

((10^w+2 - 10^w)/(10^w +
10^w+1))^x^2 = 9^100

Answer 1

10 or -10

Simplify numerator to (99/11)^x^2 = 9^100

Simplify to 9^x^2 = 9^100

x^2 = 100

x is 10 or -10

Question 2

2^x - 2^(x-1) = 1

What is x^3?

Answer 2

1

Rewrite equation:
(2^x) - (2x)(2^-1) = 1

Factor out 2^x:
2^x (1 - 1*2^-1) = 1

Simplify:
2^x (1 - 1 * 1/2) = 1

Simplify more:
2^x (1/2) = 1

2 * 1/2 = 1 so if 2^x must equal 2, x must be 1

1^3 = 1

Question 3

5,000(5,000^5,000) = ?

Answer 3

5,000^5,001

5,000^1 * 5,000^5,000 = 5,000^5,001

Question 4

(s^n + s^n + s^n + s^n) / 4^n + 4^n + 4^n + 4^n = ?

Answer 4

(s/4)^n

Factor out s^n from numerator and 4^n from denominator:
Numerator is s^n (4) and denominator is 4^n (4)

The 4s cancel out and we are left with (s^n)/(4^n) which can be rewritten as (s/4)^n

Question 5

5/(5 + √7) is equal to which of the following?

A. 25 - 5√7
B. (25 - 5√7)/18
C. (5 - 5√7)/18
D. (25 - 25√7)/18

Answer 5

B. (25 - 5√7)/18

The conjugate is the term that will complete the square in the denominator and remove the radical. In this case we multiply the numerator and denominator by
(5 - √7).

Numerator will equal 25 - 5√7. Denominator will be 25 - 7, which equals 18.

Question 6

If x, y, and z are positive and x^2 + y^2 = z^2, what is x in terms of y and z?

A. y - z
B. z^2 - y^2
C. √z^2-y^2 (both under the same sqrt sign)
D. √x - √y
E. √x^2 - √y^2

Answer 6

C. √z^2-y^2 (both under the same sqrt sign)

x^2 = z^2 - y^2

Take square root of everything and we get answer c

Question 7

Which of the following is equal to √.00000625?

A. 0.25
B. 0.025
C. 0.0025
D. 0.00025
E. 0.000025

Answer 7

C. 0.0025

Rewrite the decimal as a fraction:
625/100,000,000

Rewrite the fraction as 25^2 / 10,000^2

Convert the fraction back to a decimal: 0.0025