Question

Rewrite the expression in the form k· xⁿ

Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
2√x· 4x⁻⁵/² = ____

Answer 1

The expression 2√x · 4x⁻¹⁄₂ simplifies to 8 when employing properties of exponents and the idea that any number raised to the 0 power is 1.

Step-by-step explanation:

The expression 2√x · 4x⁻¹⁄₂ can be rewritten in the form of k · xⁿ by first simplifying each part of the expression and then combining them.

To begin with, the square root of x, represented as √x, can be expressed as x¹⁄₂. The expression 4x⁻¹⁄₂ means 4 multiplied by x to the -0.5 power (since -1/2 can be written as -0.5).

Multiplying these together, we get:

• 2(x¹⁄₂) · 4(x⁻¹⁄₂) = 2· 4 · x¹⁄₂ · x⁻¹⁄₂
• Since when we multiply powers with the same base we add the exponents, this gives us 8 · x¹⁄₂ + (-1/2), or 8 · x¹⁄₂ - 1/2.
• Adding the exponents 1/2 and -1/2 gives us 0, so the expression simplifies to 8 · x⁰, where x⁰ is equal to 1.
• We end up with 8 · 1, which simplifies further to just 8.

Therefore, the expression 2√x · 4x⁻¹⁄₂ has been rewritten as 8.