Exponential help?

Question

(b~10/b~3)~ -2

~ means power (number after is an exponent)

i do not understand how to work this problem.

Answer 1

b^10
------ =
b^3

b^7 [since a^m ÷ a^n = a^(m - n)]

(b^7)^(-2) =

b^(-14) = [since (a^m)^n = a^(m*n)]

1
------ [since a^(-n) = 1/a^n]
b^14

Answer 2

First do the indicated operation inside the parentheses. Then apply the last exponent to the result obtained from doing that.

From the law of exponents, b^10/b^3 = b^(10-3) = b^7.

Note this: For all n, b^-n = b^(0-n) = b^0/b^n = 1/b^n, because any number raised to the zero power is equal to 1.

(b^7)^-2 = b^[(7)x(-2)] = b^(-14) = b^(0-14) = 1/b^14.

So, 1/b^14 is your answer.

Answer 3

The part in parentheses is evaluated using the fact that x~a divided by x~b is always x~(a-b). In words, if you are dividing two numbers with the same base and different exponents, the answer is the same base to the power of the difference of the exponents (top minus bottom). So the part in the parentheses is b~7.
Next, a base with a negative exponent means, in words, 1 over the same base with the same positive exponent. A simple example is 2~(-3) = 1/(2~3) = 1/8. So (b~7)~-2 = 1/(b~14). This is soooooooo much easier to see if you can use actual exponents and fraction bars!

Answer 4

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Answer 5

(b^7)-2
b^-14
1/b^14