Exponent Rules Quiz
Questions: 16 · 10 minutes
1. For nonzero x and y, combine like bases in (x^5 y^2)(x^(-2) y^3).
x^7 y^5, after treating both exponent pairs as sums
x^3 y^5, after adding the exponents for each matching base
x^3 y^6, after subtracting the x exponents and multiplying the y exponents
x^(-10) y^6, after multiplying both pairs of exponents
2. What is the product x^3 × x^5?
x^8, because the exponents are added
x^15, because the exponents are multiplied
2x^8, because the two factors add a coefficient
x^2, because the smaller exponent is subtracted
3. A computer process starts with 2^7 identical units and reduces the amount by a factor of 2^3. How many units remain?
16 units, corresponding to 2^(7-3)
32 units, corresponding to 2^5
4 units, corresponding to 2^2
8 units, corresponding to 2^3
4. For a nonzero value of a, which expression equals a^9 ÷ a^4?
a^13, found by adding 9 and 4
a^5, found by subtracting 4 from 9
a^36, found by multiplying 9 by 4
a^(9/4), found by dividing the exponents
5. The equation 3^x × 3^2 = 3^7 uses equal bases. What value of x makes it true?
5, because x + 2 must equal 7
3, from subtracting 2 twice
9, because the known exponents are added
14, because 7 is multiplied by 2
6. Evaluate 27^(2/3) by taking the cube root and then squaring.
6, from multiplying the root index by the numerator
18, from multiplying 27 by two-thirds
729, because the fractional exponent acts like an exponent of 2
9, because the cube root of 27 is 3 and 3 squared is 9
7. Which form rewrites t^(-3) using only positive exponents, assuming t is nonzero?
-t^3, because the negative sign moves outside
1/(-t^3), because the denominator must become negative
1/t^3, because a negative exponent gives a reciprocal
t/3, because the exponent becomes a divisor
8. After simplifying (a^3 b^(-2)) ÷ (a^(-1) b), which expression has no negative exponents? Assume a and b are nonzero.
a^2/b, obtained by subtracting the absolute exponent values
a^4/b^3, obtained by subtracting exponents for each base
a^4/b, obtained by changing only the exponent of a
a^2/b^3, obtained by adding the denominator exponents
9. Assuming a and b are positive, take the fourth root represented by (16a^8 b^4)^(1/4).
4a^2 b, using 4 as the fourth root of 16
2a^4 b, dividing only the exponent on b by 4
2a^2 b^4, leaving the exponent on b unchanged
2a^2 b, taking the fourth root of each factor
10. If z is not zero, what does z^0 equal?
1/z because the exponent moves the base to the denominator
0 because the exponent is zero
z because a zero exponent leaves the base unchanged
1 for every permitted nonzero value of z
11. A scientific-notation calculation contains (3 × 10^4)(2 × 10^(-2)). What is the product in standard scientific notation?
6 × 10^2, from multiplying coefficients and adding exponents
6 × 10^(-8), from multiplying the powers' exponents
5 × 10^2, from adding both coefficients and exponents
6 × 10^6, from subtracting the negative exponent
12. A classmate reduces x^8 ÷ x^2 to x^4. For nonzero x, what should replace that answer?
x^10, because quotient exponents are added
x^16, because the exponents are multiplied
x^6, because the denominator exponent is subtracted
x^(8/2), because quotient exponents are divided
13. A student claims that (p^2 q^3)^2 equals p^4 q^5. Which correction identifies the proper result?
It equals p^4 q^9 because the exponent on q is squared
It equals p^4 q^6 because both inner exponents are multiplied by 2
It equals p^2 q^6 because the outer exponent applies only to q
It equals p^4 q^3 because the outer exponent applies only to p
14. A rectangle has side lengths 2x^3 units and 3x^2 units. Which expression gives its area?
5x^5 square units, from adding the coefficients and exponents
6x^6 square units, from multiplying both coefficients and exponents
6x^5 square units, from multiplying coefficients and adding exponents
6x square units, from subtracting the exponents
15. A student expands (2x^3)^2. Which result correctly applies the outer exponent to both factors?
2x^6, with only the variable squared
4x^5, with the exponents added
4x^6, with 2 squared and 3 multiplied by 2
4x^9, with the variable exponent squared
16. Apply the power-of-a-power rule to (m^2)^4.
m^6, from adding the two exponents
4m^2, from moving the outer exponent in front
m^16, from raising the inner exponent to the fourth power
m^8, from multiplying the exponents