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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.

JacobLlama·16 flashcards·15 vragen·1 weergaven

high schoolmathematicsalgebra

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What is the product rule?

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Achterkant

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 vragen)

Vraag 1 van 15

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

Termen in deze 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 = ____.

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

Vragen in deze 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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WiskundeAlgebra

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Exponent rules with examples step by step

Quiz(15 vragen)

Termen in deze set(16)

Vragen in deze set(15)

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