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

$5+\sqrt{36}-1=$

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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