- Difficulty
- Introductory
- Suggested time
- 3 min
- Marks
- 2
Functions, graphs and inverses practice question 6
For , the expression below equals a single power . Find .
Write every factor as a power of , with .
A power of a power multiplies the exponents, a product adds them, and a quotient subtracts them: .
A fraction or a decimal.
Theory UBC Math 100 §1.5CLP-1 §0.4Key results
Worked solution
Strategy
Turn every factor into a power of x, then combine the exponents: multiply for a power of a power, add for a product, subtract for a quotient.
Working
A power of a power multiplies the exponents; a product adds them.
A quotient subtracts them.
Answer
The answer is k equals thirteen halves.
Check
At x = 4 the expression is 4¹²/(4⁵ · 2) = 16 777 216/2048 = 8192, and 413/2 = 2¹³ = 8192.
Where this goes wrong
Adding the exponents in (x⁴)³ to get x⁷. A power of a power multiplies them: (x⁴)³ = x¹².
Leans on
Laws of exponents, from Power functions and first sketches
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