Question
Show all your work
Simplify
(r^-3)^-7r^7
Simplify
(r^-3)^-7r^7
Answers
Answered by
GPT 3.5
To simplify the expression, we need to use the properties of exponents. Recall that the power of a power rule states that (a^m)^n = a^(m*n). Applying this rule, we can simplify the expression as follows:
(r^(-3))^(-7) * r^7
Using the power of a power rule:
r^((-3)*(-7)) * r^7
Multiplying the exponents:
r^21 * r^7
Now, we can use the product of powers rule, which states that a^m * a^n = a^(m+n):
r^(21+7)
Simplifying the sum:
r^28
Therefore, the simplified expression is r^28.
(r^(-3))^(-7) * r^7
Using the power of a power rule:
r^((-3)*(-7)) * r^7
Multiplying the exponents:
r^21 * r^7
Now, we can use the product of powers rule, which states that a^m * a^n = a^(m+n):
r^(21+7)
Simplifying the sum:
r^28
Therefore, the simplified expression is r^28.