Podcast
Questions and Answers
Which expression is equivalent to $4^5 \cdot 2^5$?
Which expression is equivalent to $4^5 \cdot 2^5$?
- $2^{15}$ (correct)
- $4^6$
- $8^{10}$
- $6^5$
To multiply powers with different bases and different exponents, you must always adjust the base first.
To multiply powers with different bases and different exponents, you must always adjust the base first.
False (B)
Simplify the following expression: $\frac{10^3}{1000^2}$
Simplify the following expression: $\frac{10^3}{1000^2}$
1/1000
$\frac{9^3}{3^4} = $ ______
$\frac{9^3}{3^4} = $ ______
Match the equivalent expressions:
Match the equivalent expressions:
What is the simplified form of $(-4pq)^3$?
What is the simplified form of $(-4pq)^3$?
The expression $(a^5)^6$ is equivalent to $a^{11}$.
The expression $(a^5)^6$ is equivalent to $a^{11}$.
Fill in the blank to complete the equation: $30^{10} \cdot a^8 \cdot (a^2)^3 = (30 \cdot a^?) ^{10}$
Fill in the blank to complete the equation: $30^{10} \cdot a^8 \cdot (a^2)^3 = (30 \cdot a^?) ^{10}$
Solve for the missing exponent $7^4 a^8 b^2 = ( ...)^4$
Solve for the missing exponent $7^4 a^8 b^2 = ( ...)^4$
Match the scientific notation expressions with their results.
Match the scientific notation expressions with their results.
Which value for 'm' makes the equality $(-2)^{-1} + (-2)^m = 0$ true?
Which value for 'm' makes the equality $(-2)^{-1} + (-2)^m = 0$ true?
The expression $\frac{5^3}{25^3}$ simplifies to $\frac{1}{5^3}$
The expression $\frac{5^3}{25^3}$ simplifies to $\frac{1}{5^3}$
Simplify the expression $16^{10} : 32^7$.
Simplify the expression $16^{10} : 32^7$.
What is half of $16^2$?
What is half of $16^2$?
Match the expression $g^{m+3}*g^{-2+n}$ with its simplified values
Match the expression $g^{m+3}*g^{-2+n}$ with its simplified values
Which of the following is equal to $( -10ab)^2$?
Which of the following is equal to $( -10ab)^2$?
The value of expression $\frac{a^2b}{a^{-1}b^{-2}}$ equals to $a^3b^3$.
The value of expression $\frac{a^2b}{a^{-1}b^{-2}}$ equals to $a^3b^3$.
Solve for $a$: $a = 5$. What is the expression for $(-2)^{-1} + (-2)^a$?
Solve for $a$: $a = 5$. What is the expression for $(-2)^{-1} + (-2)^a$?
Simplify $36^{-3} \cdot 6^4 = $ ______
Simplify $36^{-3} \cdot 6^4 = $ ______
Match the expression $4^5+4^5$ with its simplified values
Match the expression $4^5+4^5$ with its simplified values
Flashcards
Adjusting bases
Adjusting bases
To multiply or divide powers with different bases and exponents, adjust the bases if possible.
Gelijkheid
Gelijkheid
A mathematical expression showing equality, with variables and constants.
Scientific notation
Scientific notation
Rewrite the expression in the form N x 10^n, where 1 ≤ |N| < 10 and n is an integer.
Study Notes
- Het veranderen van het grondtal kan nodig zijn bij het vermenigvuldigen of delen van machten met verschillende grondtallen en exponenten
Oefeningen met Machten
- 4⁴ · 2³ = (2²)⁴ · 2³ = 2⁸ · 2³ = 2¹¹ = 2048
- 2⁵ / 5⁵ = 5⁶ / 5⁵ = 5
- 8⁻⁵ · 2⁶ = (2³)⁻⁵ · 2⁶ = 2⁻¹⁵ · 2⁶ = 2⁻⁹ = 1/2⁹
- 10³ / 1000² = 10³ / (10³) ² = 10³ / 10⁶ = 10⁻³ = 1/1000
- 9⁴ · 27⁻² = (3²)⁴ · (3³)⁻² = 3⁸ · 3⁻⁶ = 3² = 9
- 16¹⁰ / 32⁷ = (2⁴)¹⁰ / (2⁵)⁷ = 2⁴⁰ / 2³⁵ = 2⁵ = 32
- 36⁻³ · 6⁴ = (6²)⁻³ · 6⁴ = 6⁻⁶ · 6⁴ = 6⁻² = 1/36
- 125⁻¹ / 5⁻⁵ = (5³)⁻¹ / 5⁻⁵ = 5⁻³ / 5⁻⁵ = 5² = 25
Machten op Twee Manieren Uitwerken
- 9⁴ / 3⁴ = (3²)⁴ / 3⁴ = 3⁸ / 3⁴ = 3⁴ = 81 (manier 1)
- 9⁴ / 3⁴ = (9/3)⁴ = 3⁴ = 81 (manier 2)
- 2⁻² / 8⁻² = 4⁻¹ / 2⁴ = 2⁻² / (2³)⁻² = 2⁻² / 2⁻⁶ = 2⁴ = 16 (manier 1)
- 2⁻² / 8⁻² = (⅛) / (¼) = ¼ (manier 2)
- 100⁻² / 10⁻² = (10²)⁻² / 10⁻² = 10⁻⁴ / 10⁻² = 10⁻² = 1/100 = 0.01 (manier 1)
- 100⁻² / 10⁻² = (1/10000) / (1/100) = (1/10000) * 100 = 1/100 = 0.01 (manier 2)
- 5³ / 25³ = 125 / 15625 = 1/125 (manier 1)
- 5³ / 25³ = (5/25)³ = (1/5)³ = 1/125 (manier 2)
Uitdrukkingen met Machten
- 4⁵ · 2⁵ = 8⁵
- De helft van 16² = 8²=2⁷
- 100²-50² = 3 · 50²
- 12⁸ / 4² = 3⁸ · 4⁶
- 4⁵ + 4⁵ = 2 · 4⁵
- Het dubbele van 16⁹ = 2³⁷
- (-4 · p · q)⁶ = 4096 · p⁶ · q⁶
- (a⁴)¹⁰ = a⁴⁰
- gᵐ⁺³ · g⁻²+ⁿ = gᵐ⁺ⁿ⁺¹
- (-10ab)² = 100a²b²
- 30¹⁰ · (a²)³ = (30 · 1 · a)¹⁰
- 2⁻² a¹² b⁶ = 256 a¹² b⁶ c⁻⁴
Is de onderstaande gelijkheid juist
- Onderzoek voor m = 5: m = 5
- Onderzoek voor m = 4: m = 4
Reken uit en geef het antwoord in de wetenschappelijke schrijfwijze
- (5 · 10⁻⁴) · (2 · 10⁷) = 1 · 10⁴
- (2,5 · 10⁻²) · (5 · 10⁵) = 1,25 · 10⁴
- (7 · 10³) · (3 · 10⁻¹²) = 2,1 · 10⁻⁸
- (1,5 · 10⁻⁵) · (5 · 10³) = 7,5 · 10⁻³
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