Simplify y^(-2) × y^7: Laws of Exponents Practice

Q: What happens when I multiply terms with negative exponents?

Negative exponents follow the same rules as positive exponents! Just add them like any other numbers: $ -2 + 7 = 5 $.

Q: Why do I add exponents instead of multiplying them?

The product rule states $ b^m \times b^n = b^{m+n} $. Think of it as: when bases are the same, exponents add up!

Q: Can I use this rule with any type of exponent?

Yes! This rule works for negative, positive, fractional, and even irrational exponents. The base just needs to be the same.

Q: How do I remember when to add vs multiply exponents?

Multiply same bases: add exponents. Raise a power to a power: multiply exponents. Same base = add, power of power = multiply!

Q: What if I get confused by the negative sign?

Treat negative exponents like regular negative numbers. Just be careful with your arithmetic: $ -2 + 7 = +5 $, not $ -9 $!

Exponent Multiplication with Negative Powers

$y^{-2}\times y^7=$

❤️ 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 Simplify the following problem

00:02 When multiplying powers with equal bases

00:05 The power of the result equals the sum of the powers

00:08 We'll apply this formula to our exercise, and add the powers together

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$y^{-2}\times y^7=$

Step-by-step solution

Note that we need to calculate multiplication between terms with identical bases, so we'll use the appropriate exponent law:

$b^m\cdot b^n=b^{m+n}$ Note that we can only use this law to calculate multiplication performed between terms with identical bases,

Here in the problem there is also a term with a negative exponent, but this does not pose an issue regarding the use of the aforementioned exponent law. In fact, this exponent law is valid in all cases for numerical terms with different exponents, including negative exponents, rational number exponents, and even irrational number exponents, etc.,

Let's apply it to the problem:

$y^{-2}\cdot y^7=y^{-2+7}=y^5$ Therefore the correct answer is A.

Final Answer

$y^5$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying same bases, add the exponents together
Technique: Calculate $y^{-2} \times y^7 = y^{-2+7} = y^5$
Check: Verify exponents add correctly: -2 + 7 = 5 ✓

Common Mistakes

Avoid these frequent errors

Multiplying exponents instead of adding them
Don't multiply -2 × 7 = -14 to get $y^{-14}$ ! This confuses the power rule with the product rule. Always add exponents when multiplying terms with the same base: -2 + 7 = 5.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

What happens when I multiply terms with negative exponents?

Negative exponents follow the same rules as positive exponents! Just add them like any other numbers: $-2 + 7 = 5$ .

Why do I add exponents instead of multiplying them?

The product rule states $b^m \times b^n = b^{m+n}$ . Think of it as: when bases are the same, exponents add up!

Can I use this rule with any type of exponent?

Yes! This rule works for negative, positive, fractional, and even irrational exponents. The base just needs to be the same.

How do I remember when to add vs multiply exponents?

Multiply same bases: add exponents. Raise a power to a power: multiply exponents. Same base = add, power of power = multiply!

What if I get confused by the negative sign?

Treat negative exponents like regular negative numbers. Just be careful with your arithmetic: $-2 + 7 = +5$ , not $-9$ !

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Exponents Rules 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