Question

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) = 9• __ + 3/2 (8 - __)

Answer 1

Solve the expression 16 - 8^0/5 + 4 (7^0 - 6)

16 - 8^0/5 + 4 (7^0 - 6) = ___

Answer 2

use the power rule of exponents to simplify (10^3)^6 your answer should include an exponent

Answer 3

If the expression 7^15 was simplified using the power rule of exponents which of the following would be an expanded equivalent expression

Answer 4

use the power rule of exponent to create simplified equivalent expression for (19^4)^9 your answer will include exponents

Answer 5

apple the property of negative integer exponents to solve 7 ^-3 the answer should not contain any exponent expression or decimals

Answer 6

Ap

Answer 7

apply the property of negative integer exponents to generate an expression equivalent to 3 ^-17/8 ^-14 with positive exponents only

Answer 8

apply the property of negative integer exponents to generate an expression equivalent to (7 ^-3)^7•7^20/6^-2 with only positive exponents then solve the expression provide the answer as an improper fraction with no exponents or decimals

Answer 9

A simplify your answer should contain no exponents 12 ^-5•12^7

Answer 10

To apply the zero power rule, we need to remember that any nonzero number raised to the power of zero is equal to 1. Therefore, we can simplify the expression as follows:

1. \((-33)^0 = 1\)
2. \(27^0 = 1\)

Now we can substitute these values into the expression:

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

Now we can fill in the blanks in the expression:

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

So, the equivalent expression is:

\[
9 • 1 + \frac{3}{2} (8 - 1)
\]

Answer 11

To solve the expression \(16 - \frac{8^0}{5} + 4 (7^0 - 6)\), we first apply the zero power rule, which states that any non-zero number raised to the power of zero is equal to 1.

1. Calculate \(8^0\):
\[
8^0 = 1
\]

2. Calculate \(7^0\):
\[
7^0 = 1
\]

Now, substitute these values into the expression:

\[
16 - \frac{1}{5} + 4 (1 - 6)
\]

Next, simplify \(4(1 - 6)\):

\[
1 - 6 = -5 \implies 4 \times -5 = -20
\]

Now substitute this value back into the expression:

\[
16 - \frac{1}{5} - 20
\]

Now, combine \(16\) and \(-20\):

\[
16 - 20 = -4
\]

Now, adjust for the fraction:

\[
-4 - \frac{1}{5}
\]

To combine \(-4\) and \(-\frac{1}{5}\), convert \(-4\) to a fraction with a denominator of 5:

\[
-4 = -\frac{20}{5}
\]

Now add the two fractions:

\[
-\frac{20}{5} - \frac{1}{5} = -\frac{20 + 1}{5} = -\frac{21}{5}
\]

Thus, the final result of the expression \(16 - \frac{8^0}{5} + 4 (7^0 - 6)\) is:

\[
-\frac{21}{5}
\]

Answer 12

To simplify \((10^3)^6\) using the power rule of exponents, you apply the rule that states \((a^m)^n = a^{m \cdot n}\).

In this case:

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

Now, calculate the exponent:

\[
3 \cdot 6 = 18
\]

So, we have:

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

Thus, the simplified expression is:

\[
10^{18}
\]

Answer 13

The power rule of exponents states that \(a^m = a \times a \times a \times \ldots\) (m times). Therefore, for the expression \(7^{15}\), the expanded equivalent expression would be the number 7 multiplied by itself 15 times.

In expanded form, it would be:

\[
7^{15} = 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7
\]

This is a total of 15 instances of the base 7 multiplied together.

If you have multiple choices to select from, the correct expanded equivalent expression for \(7^{15}\) should contain 15 instances of the base 7 multiplied together.

Answer 14

To simplify the expression \((19^4)^9\) using the power rule of exponents, we apply the rule that states \((a^m)^n = a^{m \cdot n}\).

So, for \((19^4)^9\), we have:

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

Now, calculate the exponent:

\[
4 \cdot 9 = 36
\]

Therefore, the simplified equivalent expression is:

\[
19^{36}
\]

Answer 15

To simplify \(7^{-3}\) using the property of negative integer exponents, we use the rule that states \(a^{-n} = \frac{1}{a^n}\).

Applying this to \(7^{-3}\):

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

Now, calculate \(7^3\):

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

Therefore:

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

So the final answer, without any exponent expressions or decimals, is:

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

Answer 16

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Answer 17

To simplify the expression \( \frac{3^{-17}}{8^{-14}} \) using the property of negative integer exponents, we can convert the negative exponents to positive exponents by applying the rule \( a^{-n} = \frac{1}{a^n} \).

Here's how we can do it step-by-step:

1. Convert the negative exponents:
\[
\frac{3^{-17}}{8^{-14}} = \frac{1}{3^{17}} \div \frac{1}{8^{14}}
\]

2. When dividing by a fraction, it’s equivalent to multiplying by its reciprocal:
\[
= \frac{1}{3^{17}} \times 8^{14}
\]

3. This can be rewritten as:
\[
= \frac{8^{14}}{3^{17}}
\]

Now, the expression \( \frac{8^{14}}{3^{17}} \) contains only positive exponents.

So, the final equivalent expression with positive exponents only is:

\[
\frac{8^{14}}{3^{17}}
\]

Answer 18

To solve the expression \((7^{-3})^7 \cdot 7^{20} / 6^{-2}\) using the property of negative integer exponents and obtain an expression with only positive exponents, we will proceed step by step.

### Step 1: Simplify \((7^{-3})^7\)
Using the power rule, \((a^m)^n = a^{m \cdot n}\):

\[
(7^{-3})^7 = 7^{-21}
\]

### Step 2: Combine the exponents of \(7\)
Now substitute back into the expression:

\[
7^{-21} \cdot 7^{20} / 6^{-2}
\]

When multiplying like bases, we add the exponents:

\[
7^{-21 + 20} = 7^{-1}
\]

### Step 3: Rewrite the entire expression
Now the expression becomes:

\[
\frac{7^{-1}}{6^{-2}}
\]

### Step 4: Convert negative exponents to positive
Using the property \(a^{-n} = \frac{1}{a^n}\):

\[
7^{-1} = \frac{1}{7} \quad \text{and} \quad 6^{-2} = \frac{1}{6^2}
\]

Rewriting the expression gives:

\[
\frac{\frac{1}{7}}{\frac{1}{6^2}} = \frac{1}{7} \cdot 6^2
\]

### Step 5: Calculate \(6^2\)
Calculating \(6^2\):

\[
6^2 = 36
\]

### Step 6: Multiply
Now we have:

\[
\frac{36}{7}
\]

### Final Answer
Thus, the simplified expression in the form of an improper fraction with no exponents or decimals is:

\[
\frac{36}{7}
\]

Answer 19

To simplify the expression \(12^{-5} \cdot 12^{7}\), we can use the property of exponents that states \(a^m \cdot a^n = a^{m+n}\).

### Step 1: Combine the exponents
\[
12^{-5} \cdot 12^{7} = 12^{-5 + 7} = 12^{2}
\]

### Step 2: Remove the exponent
Now we can simplify \(12^2\):

\[
12^2 = 12 \cdot 12 = 144
\]

### Final Answer
Thus, the simplified answer, with no exponents, is:

\[
144
\]