Question

Show ALL work to earn full credit. In your work, use the ^ symbol to show exponents. (Example: 2^3 is two to the third power)
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Simplify the expression & explain what you did with the exponents.
b^12
——
b ^4

Answer 1

Now write that all in one sentence

Answer 2

To simplify the expression \(\frac{b^{12}}{b^4}\), we will use the properties of exponents, specifically the quotient rule. The quotient rule states that when dividing two powers with the same base, you subtract the exponents.

Here are the steps:

1. **Identify the base and exponents:** The base is \(b\), and the exponents are \(12\) in the numerator and \(4\) in the denominator.

2. **Apply the quotient rule:** According to the quotient rule, we subtract the exponent in the denominator from the exponent in the numerator:
\[
\frac{b^{12}}{b^4} = b^{12-4}
\]

3. **Calculate the new exponent:** Now we perform the subtraction:
\[
12 - 4 = 8
\]
So we have:
\[
b^{12-4} = b^8
\]

4. **Write the final answer:** The simplified expression is:
\[
b^8
\]

In summary, we simplified the expression \(\frac{b^{12}}{b^4}\) to \(b^8\) by using the quotient rule of exponents which states that when dividing powers with the same base, you subtract the exponents.