Question

Simplify

(r^-3)^-7r^7

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify (r^-3)^-7r^7, we can start by using the rule of exponentiation that states when we have an exponent raised to another exponent, we can multiply the exponents.

Thus, we have (r^-3)^-7 * r^7.

Next, we apply the rule for negative exponents, which states that for any non-zero number a, a^-n is equal to 1/a^n.

Applying this rule to (r^-3)^-7, we get 1/(r^3)^-7.

Next, we multiply the exponents within the parentheses: (r^3)^-7 = r^(3*-7) = r^-21.

Now we are left with 1/r^-21 * r^7.

Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, 1/r^-21 is the same as r^21.

Thus, our expression simplifies to r^21 * r^7.

Using the rule of exponentiation that states a^m * a^n = a^(m+n), we can add the exponents: 21 + 7 = 28.

Therefore, (r^-3)^-7r^7 simplifies to r^28.