Solve 5³ ÷ 5² × 2³: Laws of Exponents Practice

Q: Why can't I use the rule that says when dividing powers with the same base, I subtract the exponents?

That rule only applies when you're dividing powers of the same base. Here we have $ 5^3 ÷ 5^2 × 2^3 $, so the $ 2^3 $ is separate. Calculate each power individually first!

Q: Do I divide first or multiply first in this problem?

Since division and multiplication have equal priority, work from left to right. So: $ 125 ÷ 25 = 5 $ first, then $ 5 × 8 = 40 $.

Q: What if I calculated the powers wrong?

Double-check each power step by step: $ 5^3 = 5 × 5 × 5 = 25 × 5 = 125 $. If your powers are wrong, your whole answer will be wrong!

Q: Can I rewrite this expression using exponent rules?

You could write $ 5^3 ÷ 5^2 = 5^1 = 5 $, but you still need to multiply by $ 2^3 = 8 $ separately to get $ 5 × 8 = 40 $.

Exponents with Order of Operations

$5^3:5^2\times2^3=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Calculate the powers

00:09 Break down and calculate the power

00:12 Continue solving one operation at a time

00:15 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5^3:5^2\times2^3=$

Step-by-step solution

In the first stage, let's calculate the powers of each of the terms:

$5^3=5\times5\times5=25\times5=125$

$5^2=5\times5=25$

$2^3=2\times2\times2=4\times2=8$

Now let's write the resulting expression:

$125:25\times8=$

Since the only operations in the expression are multiplication and division, we will solve the expression from left to right

In other words, we will divide first and then multiply:

$125:25=5$

$5\times8=40$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Calculate exponents first, then follow left-to-right for division/multiplication
Technique: $5^3 = 125$ , $5^2 = 25$ , $2^3 = 8$ before operations
Check: Substitute back: $125 ÷ 25 × 8 = 5 × 8 = 40$ ✓

Common Mistakes

Avoid these frequent errors

Applying exponent rules incorrectly to different bases
Don't try to use $5^3 ÷ 5^2 = 5^{3-2} = 5^1 = 5$ and ignore the $2^3$ = wrong setup! This only works when all terms have the same base. Always calculate each power separately first, then follow order of operations.

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 use the rule that says when dividing powers with the same base, I subtract the exponents?

That rule only applies when you're dividing powers of the same base. Here we have $5^3 ÷ 5^2 × 2^3$ , so the $2^3$ is separate. Calculate each power individually first!

Do I divide first or multiply first in this problem?

Since division and multiplication have equal priority, work from left to right. So: $125 ÷ 25 = 5$ first, then $5 × 8 = 40$ .

What if I calculated the powers wrong?

Double-check each power step by step: $5^3 = 5 × 5 × 5 = 25 × 5 = 125$ . If your powers are wrong, your whole answer will be wrong!

Can I rewrite this expression using exponent rules?

You could write $5^3 ÷ 5^2 = 5^1 = 5$ , but you still need to multiply by $2^3 = 8$ separately to get $5 × 8 = 40$ .

Why isn't the answer 100000 or one of the other choices?

Common errors lead to wrong answers: forgetting to multiply by 8 gives just 5, calculating powers wrong, or ignoring order of operations. Always work step by step carefully!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Order of Operations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime