Solve the Expression: 5² × 4 + 3³ Using Order of Operations

Q: Why can't I just solve from left to right like reading?

Mathematics has a specific order that everyone must follow so we all get the same answer! PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) ensures consistency.

Q: What does 3³ actually mean?

$ 3^3 $ means 3 × 3 × 3 = 27. The small number (exponent) tells you how many times to multiply the base number by itself.

Q: Do I multiply 25 × 4 before adding 27?

Yes! After calculating exponents, multiplication comes before addition in PEMDAS. So you get 25 × 4 = 100, then add 27 to get 127.

Q: How can I remember the order of operations?

Use the phrase "Please Excuse My Dear Aunt Sally" for PEMDAS! Or remember: Parentheses, Exponents, Multiply/Divide, Add/Subtract.

Q: What if I got 130 as my answer?

You likely added first: $ 4 + 3^3 = 4 + 27 = 31 $, then $ 5^2 × 31 = 775 $. Always do exponents first!

Order of Operations with Exponents

Solve:

$5^2\cdot4+3^3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Calculate each power separately and then solve

00:09 A power is essentially the number multiplied by itself according to the exponent

00:18 Let's break down each power into multiplications and solve

00:21 Solve one multiplication at a time and then continue

00:24 Substitute the solutions into our question and calculate

00:29 Always solve multiplication and division before addition and subtraction

00:32 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve:

$5^2\cdot4+3^3$

Step-by-step solution

Remember that according to the order of arithmetic operations, exponents precede multiplication and division, which precede addition and subtraction (and parentheses always precede everything).

So first calculate the values of the terms with exponents and then subtract the results:

$5^2\cdot4+3^3 =25\cdot4+27=100+27=127$ Therefore, the correct answer is option B.

Final Answer

127

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Calculate exponents before multiplication and addition
Technique: First compute $5^2 = 25$ and $3^3 = 27$ , then multiply and add
Check: Verify step-by-step: 25 × 4 + 27 = 100 + 27 = 127 ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following PEMDAS
Don't calculate 5 × 4 = 20 first and then square it = 8027! This ignores the order of operations and creates massive errors. Always calculate exponents first, then multiplication, then 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

Why can't I just solve from left to right like reading?

Mathematics has a specific order that everyone must follow so we all get the same answer! PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) ensures consistency.

What does 3³ actually mean?

$3^3$ means 3 × 3 × 3 = 27. The small number (exponent) tells you how many times to multiply the base number by itself.

Do I multiply 25 × 4 before adding 27?

Yes! After calculating exponents, multiplication comes before addition in PEMDAS. So you get 25 × 4 = 100, then add 27 to get 127.

How can I remember the order of operations?

Use the phrase "Please Excuse My Dear Aunt Sally" for PEMDAS! Or remember: Parentheses, Exponents, Multiply/Divide, Add/Subtract.

What if I got 130 as my answer?

You likely added first: $4 + 3^3 = 4 + 27 = 31$ , then $5^2 × 31 = 775$ . Always do exponents first!

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