Asked by No name 🫦

Solve the expression 15*8^0 /5 + 4 (7^0- 6)

15*8^0 /5 + 4 (7^0- 6) = blank
Answered by No name 🫦
Use the power rule of exponents to simplify (10^3)^6
Answered by No name 🫦
Use the power rule of exponents to create a simplified equivalent expression for (19^4)^9
Answered by No name 🫦
Apply the property of negative integer exponents to solve7^-3. The answer should not contain any exponent expressions or decimals.

7^-3 =
Answered by No name 🫦
I don’t understand
Answered by No name 🫦
So it’s 1/343
Answered by GPT-4o mini
To solve the expression \( 15 \cdot 8^0 / 5 + 4 (7^0 - 6) \), we need to evaluate it step by step.

1. **Evaluate \( 8^0 \) and \( 7^0 \):**
- Any non-zero number raised to the power of 0 is 1.
- Thus, \( 8^0 = 1 \) and \( 7^0 = 1 \).

2. **Substituting back into the expression:**
\[
15 \cdot 1 / 5 + 4 (1 - 6)
\]

3. **Simplifying the first term:**
\[
15 / 5 = 3
\]

4. **Evaluating the second term:**
\[
1 - 6 = -5
\]
Therefore, \( 4 (1 - 6) = 4 \cdot (-5) = -20 \).

5. **Combining the results:**
\[
3 + (-20) = 3 - 20 = -17
\]

So, the final result of the expression is:
\[
\boxed{-17}
\]
Answered by GPT-4o mini
To simplify \( (10^3)^6 \) using the power rule of exponents, you multiply the exponents. The power rule states that \( (a^m)^n = a^{m \cdot n} \).

Applying this rule:

\[
(10^3)^6 = 10^{3 \cdot 6} = 10^{18}
\]

Thus, the simplified expression is:

\[
\boxed{10^{18}}
\]
Answered by GPT-4o mini
To simplify \( (19^4)^9 \) using the power rule of exponents, we multiply the exponents. The power rule states that \( (a^m)^n = a^{m \cdot n} \).

Applying this rule:

\[
(19^4)^9 = 19^{4 \cdot 9} = 19^{36}
\]

Thus, the simplified equivalent expression is:

\[
\boxed{19^{36}}
\]
Answered by GPT-4o mini
To apply the property of negative integer exponents, we use the rule that states:

\[
a^{-n} = \frac{1}{a^n}
\]

Using this property for \( 7^{-3} \):

\[
7^{-3} = \frac{1}{7^3}
\]

Now we need to compute \( 7^3 \):

\[
7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343
\]

Therefore:

\[
7^{-3} = \frac{1}{7^3} = \frac{1}{343}
\]

The answer is:

\[
\boxed{\frac{1}{343}}
\]
Answered by GPT-4o mini
No problem! Let's break it down step by step to clarify how we simplify \( 7^{-3} \).

### Step 1: Understand Negative Exponents
The property of negative exponents states that when you have a negative exponent, you take the reciprocal (or "flip") of the base raised to the positive version of that exponent.

So, for any base \( a \):
- \( a^{-n} = \frac{1}{a^n} \)

### Step 2: Apply the Property to \( 7^{-3} \)
For your specific case:
- You have \( 7^{-3} \)

Using the property:
\[
7^{-3} = \frac{1}{7^3}
\]

### Step 3: Calculate \( 7^3 \)
Next, we need to calculate \( 7^3 \) (which means 7 multiplied by itself three times):
\[
7^3 = 7 \times 7 \times 7
\]

1. First, calculate \( 7 \times 7 = 49 \)
2. Then, multiply that result by 7:
\[
49 \times 7 = 343
\]

### Step 4: Substitute Back
Now we can substitute the value of \( 7^3 \) back into our expression:
\[
7^{-3} = \frac{1}{7^3} = \frac{1}{343}
\]

### Final Answer
So, the simplified answer for \( 7^{-3} \) is:
\[
\boxed{\frac{1}{343}}
\]

If you have any more questions or need further clarification, feel free to ask!
Answered by GPT-4o mini
Yes, that's correct!

The simplified value of \( 7^{-3} \) is indeed \( \frac{1}{343} \).

If you have any other questions or need further explanation, feel free to ask!