Question
1. Using the properties of exponents, which expression is equivalent to x16⋅x16
(1 point)
Responses
1x√3
the fraction with numerator 1 and denominator cube root of x
x−−√36
36th root of x
x−−√
square root of x
x−−√3
cube root of x
Question 2
2. Using the properties of exponents, which expression is equivalent to xx34
(1 point)
Responses
x
x
x−−√4
4th root of x
1x√4
the fraction with numerator 1 and denominator 4th root of x
x4
x to the 4th power
Question 3
3. Solve the following equation with a rational exponent: 2x32=16
(1 point)
Responses
8
8
64
64
4
4
no solution
no solution
Question 4
4. Solve the following equation with a rational exponent: 5x43=80
(1 point)
Responses
12
12
40.32
40.32
8
8
16
16
Question 5
5. Solve the following equation with a rational exponent: x23=64
(1 point)
Responses
512
512
32
32
8
8
16
16
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(1 point)
Responses
1x√3
the fraction with numerator 1 and denominator cube root of x
x−−√36
36th root of x
x−−√
square root of x
x−−√3
cube root of x
Question 2
2. Using the properties of exponents, which expression is equivalent to xx34
(1 point)
Responses
x
x
x−−√4
4th root of x
1x√4
the fraction with numerator 1 and denominator 4th root of x
x4
x to the 4th power
Question 3
3. Solve the following equation with a rational exponent: 2x32=16
(1 point)
Responses
8
8
64
64
4
4
no solution
no solution
Question 4
4. Solve the following equation with a rational exponent: 5x43=80
(1 point)
Responses
12
12
40.32
40.32
8
8
16
16
Question 5
5. Solve the following equation with a rational exponent: x23=64
(1 point)
Responses
512
512
32
32
8
8
16
16
Skip to navigation
Answers
GPT-4o mini
Let's go through each question step by step.
### Question 1:
Using the properties of exponents, you want to simplify \( x^{16} \cdot x^{16} \).
Using the property \( a^m \cdot a^n = a^{m+n} \):
\[
x^{16} \cdot x^{16} = x^{16+16} = x^{32}
\]
None of the provided responses seem to match \( x^{32} \). Please double-check the options listed.
---
### Question 2:
You want to simplify \( x^{x^{3/4}} \) or more likely \( x \cdot x^{3/4} \).
Using the property again \( a^m \cdot a^n = a^{m+n} \):
\[
x \cdot x^{3/4} = x^{1 + 3/4} = x^{7/4}
\]
None of the provided options appear to match \( x^{7/4} \).
---
### Question 3:
Solve the equation \( 2x^{3/2} = 16 \).
Divide both sides by 2:
\[
x^{3/2} = 8
\]
Raise both sides to the power of \( \frac{2}{3} \):
\[
x = 8^{2/3}
\]
Find \( 8^{2/3} \):
\[
8^{2/3} = (2^3)^{2/3} = 2^{3 \cdot (2/3)} = 2^2 = 4
\]
So the answer is **4**.
---
### Question 4:
Solve the equation \( 5x^{4/3} = 80 \).
Divide both sides by 5:
\[
x^{4/3} = 16
\]
Raise both sides to the power of \( \frac{3}{4} \):
\[
x = 16^{3/4}
\]
Find \( 16^{3/4} \):
\[
16^{3/4} = (2^4)^{3/4} = 2^{4 \cdot (3/4)} = 2^3 = 8
\]
So the answer is **8**.
---
### Question 5:
Solve the equation \( x^{2/3} = 64 \).
Raise both sides to the power of \( \frac{3}{2} \):
\[
x = 64^{3/2}
\]
Find \( 64^{3/2} \):
\[
64^{3/2} = (8^2)^{3/2} = 8^{2 \cdot (3/2)} = 8^3 = 512
\]
So the answer is **512**.
---
### Summary of Answers:
1. Review options for \( x^{32} \)
2. Review options for \( x^{7/4} \)
3. **4**
4. **8**
5. **512**
### Question 1:
Using the properties of exponents, you want to simplify \( x^{16} \cdot x^{16} \).
Using the property \( a^m \cdot a^n = a^{m+n} \):
\[
x^{16} \cdot x^{16} = x^{16+16} = x^{32}
\]
None of the provided responses seem to match \( x^{32} \). Please double-check the options listed.
---
### Question 2:
You want to simplify \( x^{x^{3/4}} \) or more likely \( x \cdot x^{3/4} \).
Using the property again \( a^m \cdot a^n = a^{m+n} \):
\[
x \cdot x^{3/4} = x^{1 + 3/4} = x^{7/4}
\]
None of the provided options appear to match \( x^{7/4} \).
---
### Question 3:
Solve the equation \( 2x^{3/2} = 16 \).
Divide both sides by 2:
\[
x^{3/2} = 8
\]
Raise both sides to the power of \( \frac{2}{3} \):
\[
x = 8^{2/3}
\]
Find \( 8^{2/3} \):
\[
8^{2/3} = (2^3)^{2/3} = 2^{3 \cdot (2/3)} = 2^2 = 4
\]
So the answer is **4**.
---
### Question 4:
Solve the equation \( 5x^{4/3} = 80 \).
Divide both sides by 5:
\[
x^{4/3} = 16
\]
Raise both sides to the power of \( \frac{3}{4} \):
\[
x = 16^{3/4}
\]
Find \( 16^{3/4} \):
\[
16^{3/4} = (2^4)^{3/4} = 2^{4 \cdot (3/4)} = 2^3 = 8
\]
So the answer is **8**.
---
### Question 5:
Solve the equation \( x^{2/3} = 64 \).
Raise both sides to the power of \( \frac{3}{2} \):
\[
x = 64^{3/2}
\]
Find \( 64^{3/2} \):
\[
64^{3/2} = (8^2)^{3/2} = 8^{2 \cdot (3/2)} = 8^3 = 512
\]
So the answer is **512**.
---
### Summary of Answers:
1. Review options for \( x^{32} \)
2. Review options for \( x^{7/4} \)
3. **4**
4. **8**
5. **512**