Simplify the Expression: 16^(x+4)/16^3 Using Exponent Rules

Q: Why do we subtract exponents when dividing?

Think of it as canceling out multiplication! Since $ 16^3 $ means multiply by 16 three times, dividing by $ 16^3 $ removes three multiplications from $ 16^{x+4} $.

Q: What if I get confused with the parentheses in (x+4)-3?

Just distribute the negative sign: $ (x+4) - 3 = x + 4 - 3 = x + 1 $. The parentheses around (x+4) keep that expression together as one unit.

Q: How do I remember quotient rule vs product rule?

Division = Subtraction and Multiplication = Addition. When you see a fraction bar, think subtract! When you see terms multiplied, think add!

Q: Can I use this rule with different bases like 2 and 3?

No! The quotient rule only works with identical bases. You need the same number (like 16 and 16) to subtract exponents. Different bases require different methods.

Q: What if the result has a negative exponent?

That's fine! If you got something like $ 16^{x-5} $ and x

Quotient Rule with Algebraic Exponents

Insert the corresponding expression:

$\frac{16^{x+4}}{16^3}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's keep this simple!

00:10 We will use the rule for dividing powers.

00:14 If you have a number A to the power of N, divided by the same number A to the power of M,

00:20 it's the same as A to the power of M minus N.

00:25 We'll apply this rule in our exercise.

00:28 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Insert the corresponding expression:

$\frac{16^{x+4}}{16^3}=$

Step-by-step solution

To solve this problem, we need to simplify the given expression using the rules of exponents. The expression we have is:

$\frac{16^{x+4}}{16^3}$

According to the quotient rule for exponents, when dividing like bases, you subtract the exponent of the denominator from the exponent of the numerator. This is expressed as:

$\frac{a^m}{a^n} = a^{m-n}$

In our problem, the base is 16, so we apply the quotient rule. We subtract the exponent 3 in the denominator from the exponent $x+4$ in the numerator:

$\frac{16^{x+4}}{16^3} = 16^{(x+4)-3}$

Simplify the exponent by performing the subtraction within the exponent:

$16^{(x+4)-3} = 16^{x+4-3} = 16^{x+1}$

Thus, the expression simplifies to:

$16^{x+1}$

The solution to the question is: $16^{x+1}$

Final Answer

$16^{x+1}$

Key Points to Remember

Essential concepts to master this topic

Rule: When dividing same bases, subtract exponents: $\frac{a^m}{a^n} = a^{m-n}$
Technique: Subtract denominator exponent from numerator: (x+4) - 3 = x+1
Check: Verify by expanding: $16^{x+1} = 16^x \cdot 16^1$ ✓

Common Mistakes

Avoid these frequent errors

Adding exponents instead of subtracting
Don't add (x+4) + 3 = x+7! This treats division like multiplication and gives $16^{x+7}$ . Division means subtraction in exponent rules. Always subtract the bottom exponent from the top exponent.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why do we subtract exponents when dividing?

Think of it as canceling out multiplication! Since $16^3$ means multiply by 16 three times, dividing by $16^3$ removes three multiplications from $16^{x+4}$ .

What if I get confused with the parentheses in (x+4)-3?

Just distribute the negative sign: $(x+4) - 3 = x + 4 - 3 = x + 1$ . The parentheses around (x+4) keep that expression together as one unit.

How do I remember quotient rule vs product rule?

Division = Subtraction and Multiplication = Addition. When you see a fraction bar, think subtract! When you see terms multiplied, think add!

Can I use this rule with different bases like 2 and 3?

No! The quotient rule only works with identical bases. You need the same number (like 16 and 16) to subtract exponents. Different bases require different methods.

What if the result has a negative exponent?

That's fine! If you got something like $16^{x-5}$ and x < 5, the exponent could be negative. The quotient rule still applies the same way.

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