Simplify the Expression: √5 ÷ ⁴√5 Step-by-Step

Question

Solve the following exercise:

554= \frac{\sqrt{5}}{\sqrt[4]{5}}=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 Every number is to the power of 1
00:08 Every "regular" root is of order 2
00:13 When we have a root of order (B) of a number (X) to the power of (A)
00:18 The result equals number (X) to the power of (A divided by B)
00:22 Apply this formula to our exercise
00:27 When we have division of powers (A/B) with equal bases
00:34 The result equals the common base to the power of the difference of powers (A - B)
00:38 Apply this formula to our exercise, and subtract between the powers
00:43 Determine the common denominator and calculate the power
00:58 Apply this formula again to our exercise in the opposite direction
01:02 Convert from the power to the fourth root
01:05 This is the solution

Step-by-Step Solution

Let's simplify the expression 554 \frac{\sqrt{5}}{\sqrt[4]{5}} using the rules of exponents:

  • First, we convert 5 \sqrt{5} to exponent form: 5=51/2 \sqrt{5} = 5^{1/2} .
  • Next, we convert 54 \sqrt[4]{5} to exponent form: 54=51/4 \sqrt[4]{5} = 5^{1/4} .
  • Now, divide the two expressions: 51/251/4=51/2−1/4 \frac{5^{1/2}}{5^{1/4}} = 5^{1/2 - 1/4} .
  • Subtract the exponents: 51/2−1/4=52/4−1/4=51/4 5^{1/2 - 1/4} = 5^{2/4 - 1/4} = 5^{1/4} .

The problem is simplified to 54 \sqrt[4]{5} .

Therefore, the simplified form of the given expression is 54 \sqrt[4]{5} .

Answer

54 \sqrt[4]{5}

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