Simplify d^8 / d^7, express your answer using positive exponents.
Understand the Problem
The question is asking to simplify the fraction where the numerator is d raised to the power of 8 and the denominator is d raised to the power of 7, while expressing the answer using positive exponents.
Answer
The simplified form of $\frac{d^8}{d^7}$ is $d$.
Answer for screen readers
The simplified form of $\frac{d^8}{d^7}$ is $d$.
Steps to Solve
- Identify the expression to simplify
The expression we have is $\frac{d^8}{d^7}$.
- Apply the quotient rule for exponents
According to the quotient rule, when you divide like bases with exponents, you subtract the exponent in the denominator from the exponent in the numerator.
This can be represented mathematically as:
$$ \frac{a^m}{a^n} = a^{m-n} $$
Here, for our expression:
$$ \frac{d^8}{d^7} = d^{8-7} $$
- Simplify the exponent
Now calculate the exponent:
$$ 8 - 7 = 1 $$
So we have:
$$ d^{8-7} = d^1 $$
- Express in positive exponent form
Since $d^1$ is already using a positive exponent, we can simply represent it as $d$.
The simplified form of $\frac{d^8}{d^7}$ is $d$.
More Information
The division of exponents follows a straightforward rule that simplifies calculations, particularly useful in algebra. Understanding these rules can significantly ease the process of manipulating algebraic expressions.
Tips
- Confusing the operation: Sometimes, students mistakenly add the exponents instead of subtracting them. Remember to apply the quotient rule correctly.
- Failing to simplify: After applying the exponent rules, it's essential to simplify the expression fully instead of leaving it in fractional exponent form.
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