Asked by No name 🫦

What is the missing exponents in the following equation. h^450/h? = h^215
Answered by No name 🫦
R u sure?
Answered by No name 🫦
Simplify 12^87 divide by 12^25
Answered by No name 🫦
Which one?
Answered by No name 🫦
What is the value of 6.9-2^0
Answered by No name 🫦
Apply the zero power rule to create an equivalent expression to 9* (-33)^0 + 3/2 (8 - 27^0)

9* (-33)^0 + 3/2 (8 - 27^0) = blank * blank + 3/2 ( blank - blank)
Answered by GPT-4o mini
To solve for the missing exponents in the equation \( \frac{h^{450}}{h?} = h^{215} \), we can use the properties of exponents.

When dividing two powers with the same base, you subtract the exponents:

\[
\frac{h^{450}}{h?} = h^{450 - ?}
\]

Setting this equal to \( h^{215} \) gives us the equation:

\[
h^{450 - ?} = h^{215}
\]

Since the bases are the same, we can equate the exponents:

\[
450 - ? = 215
\]

Now, we solve for the missing exponent \( ? \):

\[
? = 450 - 215 = 235
\]

Thus, the missing exponent is \( 235 \). Therefore, the equation is:

\[
h^{450}/h^{235} = h^{215}
\]
Answered by GPT-4o mini
Let's double-check the calculation step by step to ensure it's correct.

Given the equation:

\[
\frac{h^{450}}{h?} = h^{215}
\]

Using the properties of exponents, we know:

\[
\frac{h^{450}}{h?} = h^{450 - ?}
\]

Setting this equal to \( h^{215} \) gives us:

\[
h^{450 - ?} = h^{215}
\]

Since the bases are the same, we can equate the exponents:

\[
450 - ? = 215
\]

To find \( ? \), we rearrange the equation:

\[
? = 450 - 215
\]

Calculating that gives:

\[
? = 235
\]

So the missing exponent is indeed \( 235 \). The step-by-step verification confirms that the original conclusion is accurate.
Answered by GPT-4o mini
To simplify \( \frac{12^{87}}{12^{25}} \), you can use the properties of exponents. Specifically, when you divide two powers with the same base, you subtract the exponents:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

Applying this to our expression:

\[
\frac{12^{87}}{12^{25}} = 12^{87 - 25} = 12^{62}
\]

Therefore, the simplified form of \( \frac{12^{87}}{12^{25}} \) is \( 12^{62} \).
Answered by GPT-4o mini
The simplified result of \( \frac{12^{87}}{12^{25}} \) is:

\[
12^{62}
\]

So the final answer is \( 12^{62} \).
Answered by GPT-4o mini
To solve the expression \( 6.9 - 2^0 \), we first need to evaluate \( 2^0 \).

According to the properties of exponents, any non-zero number raised to the power of 0 is equal to 1. Thus:

\[
2^0 = 1
\]

Now, we substitute \( 1 \) back into the expression:

\[
6.9 - 2^0 = 6.9 - 1
\]

Calculating this gives:

\[
6.9 - 1 = 5.9
\]

Therefore, the value of \( 6.9 - 2^0 \) is \( 5.9 \).
Answered by GPT-4o mini
The zero power rule states that any non-zero number raised to the power of zero equals 1. Thus, we can simplify the expression \(9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0)\) step by step.

1. **Apply the zero power rule:**
- \((-33)^0 = 1\)
- \(27^0 = 1\)

2. **Substituting these values back into the expression:**
- \(9 \cdot (-33)^0 = 9 \cdot 1 = 9\)
- \(27^0 = 1\) thus the expression becomes:
\[
9 + \frac{3}{2}(8 - 1)
\]

3. **Now simplify \(8 - 1\):**
\[
8 - 1 = 7
\]

4. **Substituting this back into the expression:**
\[
9 + \frac{3}{2} \cdot 7
\]

5. **Now calculate \(\frac{3}{2} \cdot 7\):**
\[
\frac{3 \cdot 7}{2} = \frac{21}{2}
\]

Thus, the original expression simplifies to:

\[
9 + \frac{21}{2}
\]

Now, to match your requested format:

\[
9 \cdot (-33)^0 + \frac{3}{2} \left( 8 - 27^0 \right) = 9 \cdot 1 + \frac{3}{2}(7)
\]

So filling in the blanks gives:

\[
9 \cdot 1 + \frac{3}{2}(7)
\]

Final answer:

\[
9 \cdot 1 + \frac{3}{2}(7)
\]