Question Simplify the expression $(16x)^{1/2}$ to radical form.

Studdy Solution

STEP 1

Assumptions
1. We are given the exponential expression $(16x)^{\frac{1}{2}}$ .
2. The goal is to write this expression in simplified radical form.

STEP 2

Recognize that an exponent of $\frac{1}{2}$ is equivalent to the square root.
$a^{\frac{1}{2}} = \sqrt{a}$

STEP 3

Apply the square root to the entire expression inside the parentheses.
$\left(16x\right)^{\frac{1}{2}} = \sqrt{16x}$

STEP 4

Since the square root of a product can be expressed as the product of the square roots, we can separate the square root of 16 and the square root of x.
$\sqrt{16x} = \sqrt{16} \cdot \sqrt{x}$

STEP 5

Calculate the square root of 16, which is a perfect square.
$\sqrt{16} = 4$

STEP 6

Combine the square root of 16 with the square root of x to get the simplified radical form.
$\sqrt{16} \cdot \sqrt{x} = 4\sqrt{x}$
The exponential expression $(16x)^{\frac{1}{2}}$ in simplified radical form is $4\sqrt{x}$ .

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Question Simplify the expression $(16x)^{1/2}$ to radical form.

Studdy Solution

STEP 1

Assumptions
1. We are given the exponential expression $(16x)^{\frac{1}{2}}$ .
2. The goal is to write this expression in simplified radical form.

STEP 2

Recognize that an exponent of $\frac{1}{2}$ is equivalent to the square root.
$a^{\frac{1}{2}} = \sqrt{a}$

STEP 3

Apply the square root to the entire expression inside the parentheses.
$\left(16x\right)^{\frac{1}{2}} = \sqrt{16x}$

STEP 4

Since the square root of a product can be expressed as the product of the square roots, we can separate the square root of 16 and the square root of x.
$\sqrt{16x} = \sqrt{16} \cdot \sqrt{x}$

STEP 5

Calculate the square root of 16, which is a perfect square.
$\sqrt{16} = 4$

STEP 6

Combine the square root of 16 with the square root of x to get the simplified radical form.
$\sqrt{16} \cdot \sqrt{x} = 4\sqrt{x}$
The exponential expression $(16x)^{\frac{1}{2}}$ in simplified radical form is $4\sqrt{x}$ .

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Question Simplify the expression (16x)1/2(16x)^{1/2}(16x)1/2 to radical form.

Studdy Solution

STEP 1

Assumptions1. We are given the exponential expression (16x)12(16x)^{\frac{1}{2}}(16x)21​.2. The goal is to write this expression in simplified radical form.

STEP 2

Recognize that an exponent of 12\frac{1}{2}21​ is equivalent to the square root.a12=aa^{\frac{1}{2}} = \sqrt{a}a21​=a​

STEP 3

Apply the square root to the entire expression inside the parentheses.(16x)12=16x\left(16x\right)^{\frac{1}{2}} = \sqrt{16x}(16x)21​=16x​

STEP 4

Since the square root of a product can be expressed as the product of the square roots, we can separate the square root of 16 and the square root of x.16x=16⋅x\sqrt{16x} = \sqrt{16} \cdot \sqrt{x}16x​=16​⋅x​

STEP 5

Calculate the square root of 16, which is a perfect square.16=4\sqrt{16} = 416​=4

STEP 6

Combine the square root of 16 with the square root of x to get the simplified radical form.16⋅x=4x\sqrt{16} \cdot \sqrt{x} = 4\sqrt{x}16​⋅x​=4x​The exponential expression (16x)12(16x)^{\frac{1}{2}}(16x)21​ in simplified radical form is 4x4\sqrt{x}4x​.

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Question Simplify the expression $(16x)^{1/2}$ to radical form.

Assumptions
1. We are given the exponential expression $(16x)^{\frac{1}{2}}$ .
2. The goal is to write this expression in simplified radical form.

Recognize that an exponent of $\frac{1}{2}$ is equivalent to the square root.
$a^{\frac{1}{2}} = \sqrt{a}$

Apply the square root to the entire expression inside the parentheses.
$\left(16x\right)^{\frac{1}{2}} = \sqrt{16x}$

Since the square root of a product can be expressed as the product of the square roots, we can separate the square root of 16 and the square root of x.
$\sqrt{16x} = \sqrt{16} \cdot \sqrt{x}$

Calculate the square root of 16, which is a perfect square.
$\sqrt{16} = 4$

Combine the square root of 16 with the square root of x to get the simplified radical form.
$\sqrt{16} \cdot \sqrt{x} = 4\sqrt{x}$
The exponential expression $(16x)^{\frac{1}{2}}$ in simplified radical form is $4\sqrt{x}$ .