Exponents Lesson 1

Exponents

10.1

Power

A product of repeated factors.

​5² (-1)³ (⅓)²

Base

The base of a power is the common factor. (The large number)

​5² (-1)³ (⅓)²

Exponent

The exponent of a power indicates the number of times the base is used as a factor. (The number in the corner)

​5² (-1)³ (⅓)²

Power

Multiple Choice

A power is...

• Adding numbers

• The answer to a division problem

• A product of repeated factors

• The answer to a multiplication problem

Multiple Choice

What is the base?

$$8^2$$

• 8

• 2

• There is no base

• 64

Multiple Choice

What is the exponent?

$$4^9$$

• 4

• 9

• There is no exponent

• 36

Multiple Choice

What is the exponent?

$$12^5$$

• 12

• 5

• There is no base

• 60

Writing Expressions Using Exponents

Write each product using exponents

Writing Expressions Using Exponents

Write each product using exponents

Writing Expressions Using Exponents

Write each product using exponents

Writing Expressions Using Exponents

Write each product using exponents

Multiple Choice

Write the product using exponents.

$$2\ \times\ 2\ \times\ 2$$

• $$2^2$$

• $$2^3$$

• $$2^5$$

• 8

Multiple Choice

Write the product using exponents.

$$\frac{1}{3}\ \times\ \frac{1}{3}\ \times\ \frac{1}{3}\ \times\ \frac{1}{3}\ \times\ \frac{1}{3}$$

• $$\left(\frac{1}{3}\right)^5$$

• $$\left(\frac{1}{3}\right)^2$$

• $$\left(\frac{1}{3}\right)^6$$

• $$5\left(\frac{1}{3}\right)$$

Multiple Choice

Write the product using exponents.

$$0.3\ \times\ 0.3\ \times\ 0.3\ \times\ 0.3\ \times\ k\ \times\ k$$

• $$0.3^5\ \times\ k^5$$

• $$0.3^3\ \times\ 2k$$

• $$0.3^6\ \times\ k^3$$

• $$0.3^4\ \times\ k^2$$

Multiple Choice

Write the power in repeated multiplication.

$$7^3$$

• $$21$$

• $$7\ \times\ 7\ \times\ 7\ \times\ 7$$

• $$7\ \times\ 7\ \times\ 7$$

• $$7\ \times\ 7$$

Multiple Choice

Write the power in repeated multiplication.

$$3^4\ \times\ f^2$$

• $$3\ \times\ 3\ \times\ 3\ \times f\ \times\ f$$

• $$3\ \times\ 3\ \times f$$

• $$3\left(3\ \times\ f\right)$$

• $$3\ \times\ 3\ \times\ 3\ \times\ 3\ \times f\ \times f$$

Multiplying Exponents

When you multiply powers with the same base, add the exponents and keep the base.

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Multiplying Exponents

Simplify

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Multiplying Exponents

Simplify

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Multiple Choice

Simplify

$$3^7\ \times\ 3^8$$

• $$3^{15}$$

• $$3^{22}$$

• $$3^{78}$$

• $$3^1$$

Multiple Choice

Simplify

$$7^1\ \times\ 7^2$$

• $$7^1$$

• $$7^{23}$$

• $$7^{12}$$

• $$7^3$$

Multiple Choice

Simplify

$$12^3\ \times\ 12^6$$

• $$12^6$$

• $$12^9$$

• $$12^{36}$$

• $$12^{-3}$$

Dividing Exponents

When you divide powers with the same base, subtract the exponents and keep the base.

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Multiple Choice

Simplify

$$\frac{5^4}{5^2}$$

• $$5^2$$

• $$5^7$$

• $$5^6$$

• $$5^{42}$$

Multiple Choice

Simplify

$$\frac{\left(-3\right)^{10}}{\left(-3\right)^4}$$

• $$\left(-3\right)^4$$

• $$\left(-3\right)^9$$

• $$\left(-3\right)^6$$

• $$\left(-3\right)^7$$

Multiple Choice

Simplify

$$\frac{5^{12}}{5^{11}}$$

• $$5^2$$

• $$5^{13}$$

• $$5^{12}$$

• $$5^1$$

Power of a Power

When you have a power of a power, multiply the exponents and keep the base.

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Multiple Choice

Simplify

$$\left(8^7\right)^3$$

• $$8^{13}$$

• $$8^{21}$$

• $$8^5$$

• $$8^{10}$$

Multiple Choice

Simplify

$$\left(10^{10}\right)^6$$

• $$10^6$$

• $$10^{60}$$

• $$10^{16}$$

• $$10^4$$

Multiple Choice

Simplify

$$\left(1^2\right)^2$$

• $$1^6$$

• $$1^6$$

• $$1^4$$

• $$1^7$$

Unique Cases

When you have an exponent of zero, the value is always one.

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Multiple Choice

Simplify

$$\left(-9\right)^0$$

• $$1^{ }$$

• $$-9$$

• $$0$$

• $$\left(-9\right)^2$$

Multiple Choice

Simplify

$$\left(12\right)^0$$

• $$-12$$

• $$0$$

• $$1$$

• $$12$$

Unique Cases

When you have a negative exponent, to turn it positive, convert it to a fraction under 1.

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Multiple Choice

Simplify

$$11^{-3}$$

• $$\frac{1}{11^4}$$

• $$-11^3$$

• $$\frac{1}{11^3}$$

• $$\frac{11}{1^3}$$

Multiple Choice

Simplify

$$5^{-9}$$

• $$-5^{-9}$$

• $$-1$$

• $$\frac{1}{11^3}$$

• $$\frac{1}{5^9}$$

Multiple Choice

Simplify

$$8^{-11}$$

• $$\frac{1}{8^{11}}$$

• $$-8^{11}$$

• $$\frac{8}{11}$$

• $$1$$

Simplifying Expressions

Combine like term

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Multiple Choice

Challenge

Simplify

$$3x^2\ \times\ 2x^3$$

• $$5x^3$$

• $$32x^{23}$$

• Already in simplest

• $$6x^5$$

Multiple Choice

Challenge

Simplify

$$\frac{16g^6}{8g^8}$$

• $$8g^3$$

• $$4g^{14}$$

• Already in simplest

• $$2g^{-2}$$