Exponents

Question 1

(x^a)^a = ?

Answer 1

x^a^2

because it is a power to power you multiply

Question 2

which is greater ?

7^4 - 2^4 (A) or (7-2)^4 (B)

Answer 2

A is greater

Question 3

(x^a+b)(y^a)(y^b) = ?

Answer 3

= (xy)^a+b

when multiplying to exponent expressions with the same base, add the exponents; next, when multiplying two exponent expressions with the same exponent, multiply the bases

Question 4

using exponent rules, 6^(k +1) is also equal to what?

Answer 4

6^k * 6^1

Question 5

what is important first thing to look for with an exponent problem?

Answer 5

FACTOR!

Question 6

4^3 x 4^9 = 64^80 / 64^x

Answer 6

4^12 = 4^240 / 4^3x
240 - 12 / 3 = 76

answer x = 76

Question 7

a is not equal to 0, a is not equal to 1 and a^x / a^y = 1/a, then how can you simplify to know the relationship between x and y ?

Answer 7

a^(x-y) = 1/a

because of this you know that x-y has to be something negative so then you know that y has to be greater than x so you know x < y.

Question 8

if 2^a + 2^a + 2^a + 2^a = (2^2)^7, when what is the value of a?

Answer 8

a = 12

4(2^a) = 2^14
2^2(2^a) = 2^(2+a) = 2^14
so, 2+a = 14 and a = 12

answer a = 12

Question 9

if 2^a + 2^a + 2^a + 2^a = (2^2)^7, when what is the value of a?

Answer 9

a = 12

4(2^a) = 2^14
2^2(2^a) = 2^(2+a) = 2^14
so, 2+a = 14 and a = 12

answer a = 12