Question

Which was the most important lasting impact of Alexander’s conquests? (1 point) Responses the spread of Greek ideas around the ancient world the spread of Greek ideas around the ancient world the creation of a new empire the creation of a new empire the division of the empire among his generals the division of the empire among his generals Macedonian domination of Greece

Answer 1

Use the Product Rule of Exponents to simplify 510⋅55 (1 point) Responses 2515 25 superscript 15 baseline 550 5 superscript 50 baseline 515 5 superscript 15 baseline 2550

Answer 2

Find the numerical equivalent of 99⋅9−6 . Your answer should be written without exponents. (1 point)

Answer 3

What is the missing exponent in the following equation?h450h? = h215 (1 point)

Answer 4

Simplify 1287÷1225 .(1 point)

Answer 5

What is the missing number in this simplified exponential expression: 7?÷75=712 ?(1 point)

Answer 6

The most important lasting impact of Alexander’s conquests was the **spread of Greek ideas around the ancient world**. His conquests facilitated the Hellenization of the regions he conquered, leading to the widespread dissemination of Greek culture, language, and traditions, which influenced numerous civilizations and laid the groundwork for the cultural exchanges that shaped the Mediterranean and Near Eastern worlds for centuries to come.

Answer 7

To simplify \( 5^{10} \cdot 5^{5} \) using the Product Rule of Exponents, you add the exponents:

\[
5^{10} \cdot 5^{5} = 5^{10 + 5} = 5^{15}
\]

So the simplified expression is \( 5^{15} \).

The correct response is **\( 5^{15} \)**.

Answer 8

To find the numerical equivalent of \( 9 \cdot 9^{-6} \), we can rewrite it using the property of exponents:

\[
9 \cdot 9^{-6} = 9^{1} \cdot 9^{-6} = 9^{1 - 6} = 9^{-5}
\]

Now, to express \( 9^{-5} \) without exponents, we can write it as:

\[
9^{-5} = \frac{1}{9^{5}}
\]

Now we calculate \( 9^{5} \):

\[
9^{5} = 9 \cdot 9 \cdot 9 \cdot 9 \cdot 9 = 59049
\]

So,

\[
9^{-5} = \frac{1}{59049}
\]

Thus, the numerical equivalent of \( 9 \cdot 9^{-6} \) is:

\[
\frac{1}{59049}
\]

So, the final answer is **\( \frac{1}{59049} \)**.

Answer 9

To find the missing exponent in the equation

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

we can set the exponents equal to each other since the bases are the same:

\[
450h? = 215
\]

Dividing both sides by \(450\) to isolate \(h?\):

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

Now, simplifying \( \frac{215}{450} \):

The greatest common divisor (GCD) of \(215\) and \(450\) is \(5\).

Now we can simplify:

\[
\frac{215 \div 5}{450 \div 5} = \frac{43}{90}
\]

Thus, the missing exponent \(h?\) is:

\[
h? = \frac{43}{90}
\]

So the answer is \(h? = \frac{43}{90}\).

Answer 10

To simplify the fraction \( \frac{1287}{1225} \), we can find the greatest common divisor (GCD) of the numerator (1287) and the denominator (1225) and then divide both by the GCD.

First, we will find the GCD:

1. **Prime Factorization**:
- \( 1287 \): Since it's not immediately obvious, let's divide:
- \( 1287 \div 3 = 429 \)
- \( 429 \div 3 = 143 \)
- \( 143 \) can be factored into \( 11 \times 13 \).
- Therefore, \( 1287 = 3^2 \times 11 \times 13 \).

- \( 1225 \):
- \( 1225 = 25 \times 49 = 5^2 \times 7^2 \).

2. **GCD**: Since \(1287\) and \(1225\) have no common prime factors, the GCD is **1**.

Now we can simplify the fraction:

\[
\frac{1287}{1225} = \frac{1287 \div 1}{1225 \div 1} = \frac{1287}{1225}
\]

Since the GCD is 1, the fraction cannot be simplified further. Thus,

\[
\frac{1287}{1225}
\]

is already in its simplest form.

If desired, you could also express it as a decimal:

\[
\frac{1287}{1225} \approx 1.05.
\]

The simplified answer remains \( \frac{1287}{1225} \).

Answer 11

To solve the equation

\[
7^? \div 7^5 = 7^{12 ?}
\]

we can use the properties of exponents. When dividing with the same base, we subtract the exponents:

\[
7^{? - 5} = 7^{12 ?}
\]

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

\[
? - 5 = 12 ?
\]

Now, we need to solve for \( ? \).

1. Rearranging gives us:

\[
? - 12 ? = 5
\]

2. Combine like terms:

\[
-11 ? = 5
\]

3. Divide both sides by \(-11\):

\[
? = -\frac{5}{11}
\]

Thus, the missing number is

\[
-\frac{5}{11}.
\]