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Fill in the blank: $a^0$ is equal to ____.

$a^0 = 1$, as long as $a \neq 0$.

Difference between $a^{-m}$ and $a^m$?

$a^{-m} = \\frac{1}{a^m}$; $a^m$ is the positive power.

If $2^x = 16$, what is x?

Since $16 = 2^4$, we have $x = 4$.

What is the result of $5^4 \cdot 5^2$?

Using the product rule, we add the exponents: $4 + 2 = 6$.

What is the value of $a^0$?

Any non-zero number raised to the power of zero equals one.

Which expression equals $\\frac{b^3}{b^5}$?

Using the quotient rule: $3-5 = -2$, so $b^{-2}$.

Exponent rules with examples step by step

Understanding exponent rules is essential for simplifying expressions and solving equations in algebra. These rules help manage calculations involving powers of numbers.

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Front

What is the product rule?

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Back

When multiplying two powers with the same base, add the exponents: $\displaystyle a^m \cdot a^n = a^{m+n}$ .

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Quiz(15 questions)

Question 1 of 15

1. What is the result of $\displaystyle 5^4 \cdot 5^2$ ?

Terms in this Study Set(16)

What is the product rule?

When multiplying two powers with the same base, add the exponents: $\displaystyle a^m \cdot a^n = a^{m+n}$ .

What is the quotient rule?

When dividing two powers with the same base, subtract the exponents: $\displaystyle \\frac{a^m}{a^n} = a^{m-n}$ .

What is the power of a power rule?

When raising a power to another power, multiply the exponents: $\displaystyle (a^m)^n = a^{m \cdot n}$ .

Fill in the blank: $\displaystyle a^0$ is equal to ____.

$\displaystyle a^0 = 1$ , as long as $\displaystyle a \neq 0$ .

True or false: $\displaystyle a^{-n} = \\frac{1}{a^n}$

True, because negative exponents represent the reciprocal of the base raised to the positive exponent.

Difference between $\displaystyle a^{-m}$ and $\displaystyle a^m$ ?

$\displaystyle a^{-m} = \\frac{1}{a^m}$ ; $\displaystyle a^m$ is the positive power.

What happens when the base is multiplied?

For the same base, use the product rule: $\displaystyle ab^m \cdot ab^n = a^{m+n}$ .

What is the exponent of 1?

Any number raised to the power of 1 is itself: $\displaystyle a^1 = a$ .

Example of the power of a product rule?

For $\displaystyle (ab)^n$ , use: $\displaystyle (ab)^n = a^n \cdot b^n$ .

What is the exponent of 0?

For any non-zero base, $\displaystyle a^0 = 1$ . This means anything raised to zero equals one.

Question: What is $\displaystyle 2^3 \cdot 2^2$ ?

Use the product rule: $\displaystyle 2^3 \cdot 2^2 = 2^{3+2} = 2^5 = 32$ .

Which rule applies to $\displaystyle \\frac{x^5}{x^2}$ ?

Use the quotient rule: $\displaystyle \\frac{x^5}{x^2} = x^{5-2} = x^3$ .

What is the significance of negative exponents?

Negative exponents indicate reciprocals: $\displaystyle a^{-n} = \\frac{1}{a^n}$ .

True or false: $\displaystyle (3^2)^3 = 3^6$ .

True, because of the power of a power rule: $\displaystyle (a^m)^n = a^{m \cdot n}$ .

If $\displaystyle x^3 = 8$ , find $\displaystyle x$ .

Cube root both sides: $\displaystyle x = 2$ since $\displaystyle 2^3 = 8$ .

Fill in the blank: $a^4 \div a^2 = ____.

$\displaystyle a^4 \div a^2 = a^{4-2} = a^2$ .

Questions in this Study Set(15)

1. What is the result of $\displaystyle 5^4 \cdot 5^2$ ?

\displaystyle 5^6

\displaystyle 5^8

\displaystyle 5^{10}

\displaystyle 5^{12}

2. What is the value of $\displaystyle a^0$ ?

A.0

B.1

C.a

D.Undefined

3. Which expression equals $\displaystyle \\frac{b^3}{b^5}$ ?

\displaystyle b^{-2}

\displaystyle b^1

\displaystyle b^0

\displaystyle b^2

4. Which is NOT a property of exponents?

\displaystyle a^m \cdot a^n = a^{m+n}

\displaystyle a^{-n} = \\frac{1}{a^n}

\displaystyle a^m \div a^n = a^{m+n}

\displaystyle (a^m)^n = a^{m \cdot n}

5. Evaluate $\displaystyle \left(2^3\right)^2$ .

\displaystyle 2^5

\displaystyle 2^6

\displaystyle 2^7

\displaystyle 2^8

6. If $\displaystyle x^3 = 27$ , what is x?

A.1

B.2

C.3

D.4

7. What does $\displaystyle 5^{-2}$ equal?

A.0.2

\displaystyle \\frac{1}{25}

C.25

D.5

8. Using exponents, how can you express $\displaystyle 2 \cdot 2 \cdot 2$ ?

\displaystyle 2^2

\displaystyle 2^3

\displaystyle 2^4

\displaystyle 2^5

9. Which expression is equivalent to $\displaystyle \\frac{m^6}{m^2}$ ?

\displaystyle m^{4}

\displaystyle m^{8}

\displaystyle m^{3}

\displaystyle m^0

10. Simplify $\displaystyle (3^2 \cdot 3^3) \cdot 3^1$ . What is the exponent?

A.1

B.3

C.5

D.6

11. If $\displaystyle y^{-3} = \\frac{1}{y^3}$ , what is $\displaystyle y^{3}$ ?

\displaystyle y^3

\displaystyle \\frac{1}{y^3}

\displaystyle y^{-3}

D.Undefined

12. What is $\displaystyle (4^2)^3$ equal to?

\displaystyle 4^5

\displaystyle 4^6

\displaystyle 4^7

\displaystyle 4^8

13. Which of these expressions is equivalent to $\displaystyle a^3 \cdot a^{-3}$ ?

\displaystyle 1

\displaystyle 0

\displaystyle a^6

\displaystyle a

14. If $\displaystyle 2^x = 16$ , what is x?

A.2

B.3

C.4

D.5

15. Which is NOT true for $\displaystyle a^m \cdot a^n$ ?

\displaystyle a^{m+n}

\displaystyle a^{m-n}

\displaystyle a^m

\displaystyle a^n

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Exponent rules with examples step by step

Quiz(15 questions)

Terms in this Study Set(16)

Questions in this Study Set(15)

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