The correct answer is:
(64y^12/x^21)
Simplify the following expression, answers should have only positive exponents:
(4y^4/x^7)^3
(1 point)
Responses
(12y7x10)
open paren the fraction with numerator 12 y to the 7th power and denominator x to the 10th power close paren
(12y12x21)
open paren the fraction with numerator 12 y to the 12th power and denominator x to the 21th power close paren
(64y7x10)
open paren the fraction with numerator 64 y to the 7th power and denominator x to the 10th power close paren
(64y12x21)
open paren the fraction with numerator 64 y to the 12th power and denominator x to the 21th power close paren
5 answers
Anything raised to the power of zero is ALWAYS zero.(1 point)
Responses
True
True
False
Responses
True
True
False
False
Simplify this expression giving all positive exponents
3x^3y^-1z^-1/x^-4y^0z^0 = ?
3x^3y^-1z^-1/x^-4y^0z^0 = ?
To simplify the expression and give all positive exponents, you can move any negative exponent to the denominator and change its sign to make it positive. Additionally, any term with a zero exponent can be removed from the expression since any number (except 0) raised to the power of 0 is 1.
Starting with the expression:
3x^3y^-1z^-1/x^-4y^0z^0
In the numerator:
- x^3 remains unchanged
- Since y^0 equals 1, we can remove it from the expression
- Since z^0 equals 1, we can remove it from the expression
In the denominator:
- x^-4 becomes x^4 (changing the sign of the exponent to make it positive)
- y^-1 becomes y^1 (changing the sign of the exponent to make it positive)
- z^-1 becomes z^1 (changing the sign of the exponent to make it positive)
Simplifying further, we have:
3x^3 / (x^4 * y^1 * z^1)
To simplify the denominator, we can combine the terms with the same base:
3x^3 / (x^4yz)
Now, we can subtract the exponents of x to simplify:
3 / (x^4yz)
Therefore, the simplified expression with all positive exponents is:
3 / (x^4yz)
Starting with the expression:
3x^3y^-1z^-1/x^-4y^0z^0
In the numerator:
- x^3 remains unchanged
- Since y^0 equals 1, we can remove it from the expression
- Since z^0 equals 1, we can remove it from the expression
In the denominator:
- x^-4 becomes x^4 (changing the sign of the exponent to make it positive)
- y^-1 becomes y^1 (changing the sign of the exponent to make it positive)
- z^-1 becomes z^1 (changing the sign of the exponent to make it positive)
Simplifying further, we have:
3x^3 / (x^4 * y^1 * z^1)
To simplify the denominator, we can combine the terms with the same base:
3x^3 / (x^4yz)
Now, we can subtract the exponents of x to simplify:
3 / (x^4yz)
Therefore, the simplified expression with all positive exponents is:
3 / (x^4yz)