Question

Type "numerator" or "denominator" to complete each statement.

- x⁴ is in the _______.
- y¹⁴ is in the _______.
- z⁴ is in the _______.

The given expression, using only positive exponents. Then complete the statements that follow.
[ (x²y³)⁻¹ (x⁻²y²z)² ]², x ≠ 0, y ≠ 0, z ≠ 0.
The exponent on x is _______.
The exponent on y is _______.
The exponent on z is _______.

Answer 1

The numerator and denominator in the given expressions and the exponents of the variables are determined by applying the rules of exponents.In the expression [(x²y³)⁻¹ (x⁻²y²z)²]², applying the rules of exponents, we simplify to yz⁻²/x⁶. The exponent on x is 6, on y is 1, and on z is -2.

Step-by-step explanation:

The term 'numerator' refers to the top part of a fraction, while the term 'denominator' refers to the bottom part of a fraction. When we are given expressions with positive exponents, we can determine the exponents of each variable by looking at the given expression and applying the rules of exponents. Let's analyze the given expression step by step:

[(x²y³)⁻¹ (x⁻²y²z)²]² = (1/x²y³) (x⁻⁴y⁴z⁻²) = 1/(x²y³) * x⁻⁴y⁴z⁻² = x⁻⁶y¹z⁻² = yz⁻²/x⁶

Therefore, the exponent on x is 6, the exponent on y is 1, and the exponent on z is -2.

In this expression, the numerator is y and the denominator is x⁶z². The numerator's exponent is 1, the denominator's exponent for x is 6, and for z is -2.