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

Question

15*8^0 /5 + 4 (7^0- 6) = blank

Answer 1

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: \[ \boxed{-17} \]

Answer 2

Use the power rule of exponents to simplify (10^3)^6

Answer 3

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:

\[ \boxed{10^{18}} \]

Answer 4

Use the power rule of exponents to create a simplified equivalent expression for (19^4)^9

Answer 5

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:

\[ \boxed{19^{36}} \]

Answer 6

Apply the property of negative integer exponents to solve7^-3. The answer should not contain any exponent expressions or decimals.

7^-3 =

Answer 7

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:

\[ \boxed{\frac{1}{343}} \]

Answer 8

I don’t understand

Answer 9

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!

Answer 10

So it’s 1/343

Answer 11

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!