Solve (1/4)² + 1/16: Computing Squares and Sums of Fractions

Q: How do I square a fraction like (1/4)²?

Square both the numerator and denominator separately: $ (\frac{1}{4})^2 = \frac{1^2}{4^2} = \frac{1}{16} $. Don't forget to apply the exponent to both parts!

Q: Why can't I just add 1/4 + 1/16 directly?

Because of order of operations! Powers (exponents) must be calculated before addition. If you add first, you're solving a completely different problem.

Q: Do I need a common denominator to add 1/16 + 1/16?

No! Since both fractions already have the same denominator (16), just add the numerators: $ \frac{1+1}{16} = \frac{2}{16} $.

Q: How do I simplify 2/16 to get the final answer?

Find the greatest common factor of 2 and 16, which is 2. Divide both numerator and denominator by 2: $ \frac{2÷2}{16÷2} = \frac{1}{8} $.

Q: What if I forgot PEMDAS and got a different answer?

Don't worry! This is a common mistake. Remember PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Always do exponents before addition!

Fraction Powers with Addition Operations

$(\frac{1}{4})^2+\frac{1}{16}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:05 When raising a fraction to a power, both numerator and denominator are raised to that power

00:11 Let's calculate the powers

00:21 Add

00:29 Break down 16 into factors 8 and 2

00:37 Reduce wherever possible

00:43 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(\frac{1}{4})^2+\frac{1}{16}=$

Step-by-step solution

Let's solve the problem step-by-step using the order of operations, specifically addressing powers and fractions.

Given the expression: $(\frac{1}{4})^2+\frac{1}{16}$

First, evaluate the power: $(\frac{1}{4})^2$
Squaring a fraction means squaring both the numerator and the denominator:
$(\frac{1}{4})^2 = \frac{1^2}{4^2} = \frac{1}{16}$
Next, add the fractions: $\frac{1}{16} + \frac{1}{16}$
Since the denominators are the same, simply add the numerators:
$\frac{1+1}{16} = \frac{2}{16} = \frac{1}{8}$

Therefore, the value of the expression is $\frac{1}{8}$ .

Final Answer

1/8

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Always evaluate powers before addition in expressions
Squaring Fractions: $(\frac{1}{4})^2 = \frac{1^2}{4^2} = \frac{1}{16}$
Verification: Add $\frac{1}{16} + \frac{1}{16} = \frac{2}{16} = \frac{1}{8}$ ✓

Common Mistakes

Avoid these frequent errors

Adding before squaring the fraction
Don't try to add $\frac{1}{4} + \frac{1}{16}$ first = wrong result! This ignores the exponent and breaks order of operations. Always evaluate powers first, then perform addition.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

$36-4\div2$

FAQ

Everything you need to know about this question

How do I square a fraction like (1/4)²?

Square both the numerator and denominator separately: $(\frac{1}{4})^2 = \frac{1^2}{4^2} = \frac{1}{16}$ . Don't forget to apply the exponent to both parts!

Why can't I just add 1/4 + 1/16 directly?

Because of order of operations! Powers (exponents) must be calculated before addition. If you add first, you're solving a completely different problem.

Do I need a common denominator to add 1/16 + 1/16?

No! Since both fractions already have the same denominator (16), just add the numerators: $\frac{1+1}{16} = \frac{2}{16}$ .

How do I simplify 2/16 to get the final answer?

Find the greatest common factor of 2 and 16, which is 2. Divide both numerator and denominator by 2: $\frac{2÷2}{16÷2} = \frac{1}{8}$ .

What if I forgot PEMDAS and got a different answer?

Don't worry! This is a common mistake. Remember PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Always do exponents before addition!

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