Photo AI

Find the value of $8^{\frac{4}{3}}$ - Edexcel - A-Level Maths Pure - Question 4 - 2007 - Paper 1

Question icon

Question 4

Find-the-value-of-$8^{\frac{4}{3}}$-Edexcel-A-Level Maths Pure-Question 4-2007-Paper 1.png

Find the value of $8^{\frac{4}{3}}$. Simplify $$\frac{15x^{\frac{4}{3}}}{3x}$$.

Worked Solution & Example Answer:Find the value of $8^{\frac{4}{3}}$ - Edexcel - A-Level Maths Pure - Question 4 - 2007 - Paper 1

Step 1

Find the value of $8^{\frac{4}{3}}$

96%

114 rated

Answer

To solve for 8438^{\frac{4}{3}}, we can rewrite it using the property of exponents:

  1. Start by breaking it into two parts: 843=(813)48^{\frac{4}{3}} = (8^{\frac{1}{3}})^4

  2. Find 8138^{\frac{1}{3}}, which is the cube root of 8: 813=28^{\frac{1}{3}} = 2

  3. Raise 2 to the power of 4: (2)4=16(2)^4 = 16

Thus, the value of 8438^{\frac{4}{3}} is 16.

Step 2

Simplify $$\frac{15x^{\frac{4}{3}}}{3x}$$.

99%

104 rated

Answer

To simplify the expression:

  1. Divide the coefficients: 153=5\frac{15}{3} = 5

  2. Simplify the variable part: x43x=x43−1=x43−33=x13\frac{x^{\frac{4}{3}}}{x} = x^{\frac{4}{3}-1} = x^{\frac{4}{3}-\frac{3}{3}} = x^{\frac{1}{3}}

  3. Combine both parts: 15x433x=5x13\frac{15x^{\frac{4}{3}}}{3x} = 5x^{\frac{1}{3}}

Therefore, the simplified expression is 5x135x^{\frac{1}{3}}.

Join the A-Level students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;