Simplify the following expression, answers should have only positive exponents:
(4y^4\x^7)^3
Responses
(12y^7\x^10)
open paren the fraction with numerator 12 y to the 7th power and denominator x to the 10th power close paren
(12y^12\x^21)
open paren the fraction with numerator 12 y to the 12th power and denominator x to the 21th power close paren
(64y^12\x^21)
open paren the fraction with numerator 64 y to the 12th power and denominator x to the 21th power close paren
(64y^7\x^10)
open paren the fraction with numerator 64 y to the 7th power and denominator x to the 10th power close paren
(64y^7\x^10)
To simplify the expression (4y^4\x^7)^3 and get a positive exponent for all terms, we follow the rules of exponentiation.
First, we raise each term inside the parentheses to the power of 3:
(4^3) * (y^4)^3 * (x^7)^3
Next, we simplify each term raised to the power of 3:
64 * y^(4 * 3) * x^(7 * 3)
Now, we simplify the exponents:
64 * y^12 * x^21
Therefore, the simplified expression is (64y^12\x^21).