Question
Using the properties of exponents, which expression is equivalent to x16⋅x16
(1 point)
Responses
x−−√
square root of x
x−−√36
36th root of x
x−−√3
cube root of x
1x√3
the fraction with numerator 1 and denominator cube root of x
Question 2
Using the properties of exponents, which expression is equivalent to xx34
(1 point)
Responses
x−−√4
4th root of x
x4
x to the 4th power
1x√4
the fraction with numerator 1 and denominator 4th root of x
x
x
Question 3
Solve the following equation with a rational exponent: 2x32=16
(1 point)
Responses
4
4
8
8
no solution
no solution
64
64
Question 4
Solve the following equation with a rational exponent: 5x34=80
(1 point)
Responses
8
8
16
16
40.32
40.32
12
12
Question 5
Solve the following equation with a rational exponent: x23=64
(1 point)
Responses
32
32
16
16
512
512
8
8
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(1 point)
Responses
x−−√
square root of x
x−−√36
36th root of x
x−−√3
cube root of x
1x√3
the fraction with numerator 1 and denominator cube root of x
Question 2
Using the properties of exponents, which expression is equivalent to xx34
(1 point)
Responses
x−−√4
4th root of x
x4
x to the 4th power
1x√4
the fraction with numerator 1 and denominator 4th root of x
x
x
Question 3
Solve the following equation with a rational exponent: 2x32=16
(1 point)
Responses
4
4
8
8
no solution
no solution
64
64
Question 4
Solve the following equation with a rational exponent: 5x34=80
(1 point)
Responses
8
8
16
16
40.32
40.32
12
12
Question 5
Solve the following equation with a rational exponent: x23=64
(1 point)
Responses
32
32
16
16
512
512
8
8
Skip to navigation
Answers
Answered by
GPT-4o mini
Let's go through each question one by one.
### Question 1:
**Using the properties of exponents, which expression is equivalent to \( x^{16} \cdot x^{16} \)?**
Using the property of exponents that states \( a^m \cdot a^n = a^{m+n} \),
\[
x^{16} \cdot x^{16} = x^{16+16} = x^{32}.
\]
Now, let's check the responses given:
- \( x^{-\sqrt{}} \) (seems unclear)
- \( x^{-\sqrt{36}} \)
- \( x^{-\sqrt{3}} \)
- \( \frac{1}{x^{\sqrt{3}}} \)
None of these options simplify to \( x^{32} \). Therefore, we need to revisit the question and responses as they seem unclear or incorrectly represented.
### Question 2:
**Using the properties of exponents, which expression is equivalent to \( x^{x^{34}} \)?**
If we consider the interpretation from the inputs, it seems there was confusion in matching this exponent.
In terms of simplification, we should be considering the following:
\[
x^{34} \text{ is itself,}
\]
and the only option from the responses that looks like it represents a power of \( x \) appropriately is:
- \( x^4 \).
Thus the best fit here appears to be:
- **\( x^4 \)**.
### Question 3:
**Solve the following equation with a rational exponent: \( 2x^{3/2} = 16 \)**
First, divide both sides by 2:
\[
x^{3/2} = 8.
\]
Now, raise both sides to the power of \( \frac{2}{3} \):
\[
x = 8^{2/3}.
\]
Calculating \( 8^{2/3} \):
\[
8^{1/3} = 2 \implies 8^{2/3} = 2^2 = 4.
\]
Thus, the solution is:
- **4**.
### Question 4:
**Solve the following equation with a rational exponent: \( 5x^{3/4} = 80 \)**
First, divide both sides by 5:
\[
x^{3/4} = 16.
\]
Now, raise both sides to the power of \( \frac{4}{3} \):
\[
x = 16^{4/3}.
\]
Calculating \( 16^{4/3} \):
\[
16^{1/3} = 2 \implies 16^{4/3} = 2^4 = 16.
\]
Thus, the solution is:
- **16**.
### Question 5:
**Solve the following equation with a rational exponent: \( x^{2/3} = 64 \)**
Raise both sides to the power of \( \frac{3}{2} \):
\[
x = 64^{3/2}.
\]
Calculating \( 64^{3/2} \):
\[
64^{1/2} = 8 \implies 64^{3/2} = 8^3 = 512.
\]
Thus, the solution is:
- **512**.
Please verify responses with expected findings since there’s an ambiguity in certain definitions in the response layouts provided.
### Question 1:
**Using the properties of exponents, which expression is equivalent to \( x^{16} \cdot x^{16} \)?**
Using the property of exponents that states \( a^m \cdot a^n = a^{m+n} \),
\[
x^{16} \cdot x^{16} = x^{16+16} = x^{32}.
\]
Now, let's check the responses given:
- \( x^{-\sqrt{}} \) (seems unclear)
- \( x^{-\sqrt{36}} \)
- \( x^{-\sqrt{3}} \)
- \( \frac{1}{x^{\sqrt{3}}} \)
None of these options simplify to \( x^{32} \). Therefore, we need to revisit the question and responses as they seem unclear or incorrectly represented.
### Question 2:
**Using the properties of exponents, which expression is equivalent to \( x^{x^{34}} \)?**
If we consider the interpretation from the inputs, it seems there was confusion in matching this exponent.
In terms of simplification, we should be considering the following:
\[
x^{34} \text{ is itself,}
\]
and the only option from the responses that looks like it represents a power of \( x \) appropriately is:
- \( x^4 \).
Thus the best fit here appears to be:
- **\( x^4 \)**.
### Question 3:
**Solve the following equation with a rational exponent: \( 2x^{3/2} = 16 \)**
First, divide both sides by 2:
\[
x^{3/2} = 8.
\]
Now, raise both sides to the power of \( \frac{2}{3} \):
\[
x = 8^{2/3}.
\]
Calculating \( 8^{2/3} \):
\[
8^{1/3} = 2 \implies 8^{2/3} = 2^2 = 4.
\]
Thus, the solution is:
- **4**.
### Question 4:
**Solve the following equation with a rational exponent: \( 5x^{3/4} = 80 \)**
First, divide both sides by 5:
\[
x^{3/4} = 16.
\]
Now, raise both sides to the power of \( \frac{4}{3} \):
\[
x = 16^{4/3}.
\]
Calculating \( 16^{4/3} \):
\[
16^{1/3} = 2 \implies 16^{4/3} = 2^4 = 16.
\]
Thus, the solution is:
- **16**.
### Question 5:
**Solve the following equation with a rational exponent: \( x^{2/3} = 64 \)**
Raise both sides to the power of \( \frac{3}{2} \):
\[
x = 64^{3/2}.
\]
Calculating \( 64^{3/2} \):
\[
64^{1/2} = 8 \implies 64^{3/2} = 8^3 = 512.
\]
Thus, the solution is:
- **512**.
Please verify responses with expected findings since there’s an ambiguity in certain definitions in the response layouts provided.
There are no human answers yet. A form for humans to post answers is coming very soon!