Exponents Quiz
Questions: 16 · 10 minutes
1. When the power-of-a-power rule is applied to (a^2)^3, what is the result?
a^5, using exponent addition
3a^2, treating the outer power as a coefficient
a^8, raising the exponent itself to the third power
a^6, using exponent multiplication
2. For nonzero m and n, simplify (m^5 n^2)/(m^2 n^(-1)).
m^3 n, subtracting 1 instead of negative 1 for n
m^3/(n^3), placing the resulting n factor in the denominator
m^7 n, adding the exponents of m
m^3 n^3, subtracting denominator exponents from numerator exponents
3. For y not equal to zero, simplify y^8 divided by y^3.
y^24, from multiplying the exponents
y^11, from adding the exponents
y^5, from subtracting the exponents
y^(8/3), from dividing the exponents
4. A culture starts with 50 cells and doubles once per hour. The four-hour model is 50 × 2^4. How many cells does it predict?
400 cells, using three doublings
800 cells, using four doublings
200 cells, multiplying 50 by 4
1,600 cells, using five doublings
5. A simplification step combines x^3 × x^4. What should replace the product?
x^12, found by multiplying the exponents
x^1, found by subtracting the exponents
2x^7, found by adding a coefficient
x^7, found by adding the exponents
6. Which expanded product represents 3^4?
Three factors of 4: 4 × 4 × 4
Four factors of 3: 3 × 3 × 3 × 3
The base times the exponent: 3 × 4
Four added terms: 3 + 3 + 3 + 3
7. For nonzero x, how can the reciprocal 1/(x^6) be written using a negative exponent?
x^(-6), which moves x^6 across the fraction bar
x^6, which is the original denominator factor
-x^6, which changes the sign rather than taking a reciprocal
6x^(-1), which incorrectly turns the exponent into a coefficient
8. A formula contains b^0, where b is nonzero. Which value can be substituted for b^0?
The unchanged base b
The number zero
The number one
The opposite of the base, -b
9. A cube-root-and-power calculation is written as 8^(2/3). What is its value?
4, because the cube root of 8 is 2 and 2 squared is 4
8/3, from treating the fractional exponent as division
2, from applying only the cube-root operation
16, from applying only the square operation
10. A square has side length 3x^2, with x positive. Which expression gives its area?
6x^4, doubling the coefficient
9x^2, squaring only the coefficient
9x^4, squaring the entire side length
3x^4, squaring only the variable factor
11. Which positive fraction is equivalent to 2^(-3)?
1/6, the reciprocal of 2 × 3
1/8, the reciprocal of 2^3
3/2, formed by reversing the base and exponent
8/1, the positive-power value
12. A scientific-notation calculation contains (4 × 10^3)(2 × 10^(-5)). What is the product?
8 × 10^(-15), from multiplying the exponents
6 × 10^(-2), from adding the leading numbers
8 × 10^2, from ignoring the negative sign
8 × 10^(-2), from multiplying 4 by 2 and adding the exponents
13. A student writes 2^3 + 2^4 = 2^7, saying that exponents should be added. Which evaluation is accurate?
The work is correct because both terms have base 2.
The rule was misapplied: exponents add when like bases are multiplied, while this sum equals 24.
The exponents should instead be multiplied, making the result 2^12.
The addition rule was misapplied, but the correct sum is 2^5.
14. An equation is written as 2^n = 32. Which value solves for n?
n = 5, because 2^5 equals 32
n = 6, because this would produce 64
n = 4, because this would produce 16
n = 16, obtained by dividing 32 by 2
15. Four powers are being compared. Which one has the greatest value?
3^4, which equals 81
5^2, which equals 25
4^3, which equals 64
2^6, which also equals 64
16. Using the principal nonnegative square root, evaluate 81^(1/2).
40.5, obtained by dividing 81 by 2
8, one less than the square root
9, because 9 squared is 81
27, obtained by dividing 81 by 3