Free Printable Exponent Calculations

1.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.

Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

2.

4³x 4³

a)

4⁶

b)

4⁹

c)

16⁶

d)

16⁹

3.

Simplify: (x⁸)(x^-5)

a)

x^-40

b)

x^-13

c)

x¹³

d)

x³

4.

According to exponent rules, when we raise a power to a power we _______ the exponents. Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

5.

Select the expression that is equivalent (equal) to (7⁶)⁴.

a)

7¹⁰

b)

7²

c)

7²⁴

d)

7²⁷

6.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

7.

(34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

8.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

9.

(34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

10.

According to exponent rules, when we divide two powers with the same base we _______ the exponents. Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

11.

Select the expression equivalent (equal) to $\frac{6^8}{6^3}$ .

a)

$6^{11}$

b)

$6^5$

c)

$6^{24}$

d)

$6^{-5}$

12.

Which expression is equivalent (equal) to $\frac{10^{-3}}{10^9}$ .

a)

$10^{-12}$

b)

$10^{-6}$

c)

$10^6$

d)

$10^{-27}$

13.

Simplify the expression using the properties of exponents. $\frac{t^{12}u^7}{t^2u}$

a)

$t^{14}u^8$

b)

$t^{24}u^7$

c)

$t^{10}u^7$

d)

$t^{10}u^6$

14.

Which expression is equivalent (equal) to $\frac{\left(6^{-4}\right)^{-2}}{6^2}$ .

a)

$6^6$

b)

$6^{-10}$

c)

$6^{-8}$

d)

$6^{10}$

15.

When you see the multiplication of exponents ex. $10^n\cdot10^m$ , you keep the (a) the same and (b) the exponents.

Choose from the below words

base

exponent

add

multiply

16.

When MULTIPLYING EXPONENTS with the same base,

(a) the (b)

(c) the (d)

Choose from the below words

BASE

Add

Keep

Exponents

Subtract

Multiply

Divide

17.

When dividing powers with the same base, what do we do with our exponents? (a)

Choose from the below words

Subtract

Add

Multiply

Divide

18.

When DIVIDING Exponents with the same base,

(a) the (b)

(c) the (d)

Choose from the below words

BASE

Add

Keep

Exponents

Subtract

Multiply

Divide

19.

Anything raised to a power of zero is always:

(a)

Choose from the below words

1

0

itself

negative

20.

Câu 7. Kết quả của phép tính $\left(-2023\right)^0$ là:

21.

Evaluate $6^0$

22.

Simplify

a)

\frac{x^{28}y^{12}}{x^2y}

b)

$\frac{x^{28}y^{12}}{x^8y^4}$

c)

$x^{20}y^8$

23.

$3^{\left(-3a-1\right)}=243$

When looking at the equation above can 243 be expressed as base 3 to a power?

a)

Yes

b)

No

24.

$3^{\left(-3a-1\right)}=243$

$3^{\left(-3a-1\right)}=3^?$

What is the exponent we are looking for?

a)

x

b)

2

c)

-5

d)

5

25.

$3^{\left(-3a-1\right)}=3^5$
What should we do next?

a)

Take the logarithm of both sides.

b)

Set the exponents equal to each other.

26.

$3^{\left(-3a-1\right)}=3^5$
$-3a-1=5$
What is the value of $a$ ?

a)

$6$

b)

$-2$

c)

$\frac{7}{4}$

d)

$-3$

27.

$Solve\ the\ equation$
$5^{\left(-2a-3\right)}=25$
$a=?$

a)

$-\frac{5}{2}$

b)

$-\frac{1}{7}$

c)

$\frac{15}{8}$

d)

$\frac{3}{2}$

28.

$4^{\left(x-1\right)}=64^{\left(2x-2\right)}$
Which is the correct way to rewrite the equation using like bases?

a)

$4^{\left(x-1\right)}=\left(4^2\right)^{\left(2x-2\right)}$

b)

$4^{\left(x-1\right)}=\left(4^3\right)^{\left(2x-2\right)}$

29.

Which is the correct way to solve the equation?

a)

$4^{\left(x-1\right)}=\left(4^3\right)^{\left(2x-2\right)}$

$4^{\left(x-1\right)}=4^{\left(6x-6\right)}$

$x-1=6x-6$

b)

$4^{\left(x-1\right)}=\left(4^3\right)^{\left(2x-2\right)}$

$4^{\left(x-1\right)}=4^{\left(6x-2\right)}$

$x-1=6x-2$

30.

$4^{\left(x-1\right)}=\left(4^3\right)^{\left(2x-2\right)}$

$4^{\left(x-1\right)}=4^{\left(6x-6\right)}$

x-1=6x-6

What is the value of x?

a)

$-4$

b)

$1$

c)

$3$

d)

$-10$

31.

$64^{\left(2n+1\right)}=16^{\left(2n+2\right)}$
What is the value of n?

a)

$-\frac{8}{7}$

b)

$\frac{7}{5}$

c)

$\frac{1}{2}$

d)

$\frac{1}{10}$

32.

$5^x=18$
Can you get both sides of the equation with the same base?

a)

Yes

b)

No

Exponent Calculations

Total questions: 32

Worksheet time: 51mins

Similar Resources on Wayground