Can you add exponents with the same base?
Understand the Problem
The question is asking whether it is possible to add exponents that have the same base. In mathematical terms, when you have terms with the same base, you can combine them by adding their exponents. This is a fundamental property of exponents in mathematics.
Answer
Yes, you can add exponents with the same base: $a^m \cdot a^n = a^{m+n}$.
Answer for screen readers
Yes, you can add exponents with the same base, following the rule:
$$ a^m \cdot a^n = a^{m+n} $$
Steps to Solve
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Identifying the Property of Exponents
When working with exponents, the key property to remember is that if you have the same base, you can add the exponents. This can be expressed as:
$$ a^m \cdot a^n = a^{m+n} $$
This means that if you have two expressions with the same base ( a ), raised to powers ( m ) and ( n ), you can combine them by summing the exponents. -
Applying the Property
For example, if you are given ( 2^3 ) and ( 2^4 ), you can combine these as follows:
$$ 2^3 \cdot 2^4 = 2^{3 + 4} = 2^7 $$
So the result of multiplying ( 2^3 ) and ( 2^4 ) is ( 2^7 ). -
Conclusion
Therefore, it is indeed possible to add exponents when the bases are identical. Just remember to add the exponent values together while keeping the base the same.
Yes, you can add exponents with the same base, following the rule:
$$ a^m \cdot a^n = a^{m+n} $$
More Information
This property of exponents is used frequently in algebra, particularly when simplifying expressions or solving equations. It helps in reducing complexity and making calculations easier.
Tips
- A common mistake is thinking that you can simply add or subtract the bases instead of the exponents. To combine exponents, the bases must remain the same.
- Another mistake is misunderstanding when to multiply and when to add exponents; remember that multiplication of terms with the same base allows for exponent addition.
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