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Questions and Answers
Which expression is equivalent to $4^5 \times 4^{-2}$?
Which expression is equivalent to $4^5 \times 4^{-2}$?
- $4^{-10}$
- $4^{7}$
- $4^{3}$ (correct)
- $4^{-3}$
What is the simplified form of the expression $\frac{9^5}{9^2}$?
What is the simplified form of the expression $\frac{9^5}{9^2}$?
- $9^{3}$ (correct)
- $9^{\frac{5}{2}}$
- $\frac{1}{9^3}$
- $9^{7}$
Simplify the expression $(5^2)^3$.
Simplify the expression $(5^2)^3$.
- $5^6$ (correct)
- $5^5$
- $5^8$
- $5^{23}$
Which of the following is equivalent to $x^{-4}$?
Which of the following is equivalent to $x^{-4}$?
Evaluate the expression $2^0 + 3^{-1}$.
Evaluate the expression $2^0 + 3^{-1}$.
Which of the following expressions is equivalent to $\sqrt{16x^4}$?
Which of the following expressions is equivalent to $\sqrt{16x^4}$?
What is the value of $(2^{-1} + 2^{-2})^{-1}$?
What is the value of $(2^{-1} + 2^{-2})^{-1}$?
Which expression does NOT simplify to $5^3$?
Which expression does NOT simplify to $5^3$?
What is the simplified form of $\frac{a^5b^{-2}}{a^2b^3}$?
What is the simplified form of $\frac{a^5b^{-2}}{a^2b^3}$?
Simplify: $\frac{(x^2y^3)^2}{x^3y}$
Simplify: $\frac{(x^2y^3)^2}{x^3y}$
If $x = 2$ and $y = 3$, what is the value of $x^2y^{-1}$?
If $x = 2$ and $y = 3$, what is the value of $x^2y^{-1}$?
Which of the following is equal to $81^{\frac{3}{4}}$?
Which of the following is equal to $81^{\frac{3}{4}}$?
Simplify the expression: $\sqrt[3]{27a^6b^9}$
Simplify the expression: $\sqrt[3]{27a^6b^9}$
Which of the following expressions is equivalent to $\frac{1}{(5x)^{-2}}$?
Which of the following expressions is equivalent to $\frac{1}{(5x)^{-2}}$?
What is the value of $\frac{4^5 \cdot 4^{-2}}{4^0}$?
What is the value of $\frac{4^5 \cdot 4^{-2}}{4^0}$?
Simplify: $(a^{-2}b^3)^0 \cdot a^4b^{-1}$
Simplify: $(a^{-2}b^3)^0 \cdot a^4b^{-1}$
What is the simplified form of $\frac{x^{\frac{1}{2}} \cdot x^{\frac{3}{4}}}{x^{\frac{1}{4}}}$?
What is the simplified form of $\frac{x^{\frac{1}{2}} \cdot x^{\frac{3}{4}}}{x^{\frac{1}{4}}}$?
Which of the following expressions is equivalent to $\sqrt{\frac{x^6}{y^4}}$?
Which of the following expressions is equivalent to $\sqrt{\frac{x^6}{y^4}}$?
If $a = 4$, what is the value of $\frac{a^{2.5}}{a^{0.5}}$?
If $a = 4$, what is the value of $\frac{a^{2.5}}{a^{0.5}}$?
Given $x > 0$, simplify $\frac{(x^3)^{\frac{1}{2}}}{x^{-\frac{1}{2}}}$
Given $x > 0$, simplify $\frac{(x^3)^{\frac{1}{2}}}{x^{-\frac{1}{2}}}$
Flashcards
Product of Powers Rule
Product of Powers Rule
When multiplying powers with the same base, add the exponents: x^m * x^n = x^(m+n).
Quotient of Powers Rule
Quotient of Powers Rule
When dividing powers with the same base, subtract the exponents: x^m / x^n = x^(m-n).
Power of a Power Rule
Power of a Power Rule
To raise a power to a power, multiply the exponents: (x^m)^n = x^(m*n).
What is 10^6?
What is 10^6?
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What is 10^8 - 10^2?
What is 10^8 - 10^2?
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What is 10^3 * 10 * 10^2?
What is 10^3 * 10 * 10^2?
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What is 10^9 / 10^3?
What is 10^9 / 10^3?
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Study Notes
- Expressions equivalent to 10⁶:
10⁸ – 10²
- 10⁸ – 10² = 100,000,000 - 100 = 99,999,900
- 10⁶ = 1,000,000
- So this expression is NOT equivalent to 10⁶
10³ ⋅ 10 ⋅ 10²
- 10³ ⋅ 10 ⋅ 10² = 1000 * 10 * 100 = 1,000,000
- So this expression equals 10⁶
10⁹/10³
- 10⁹/10³ = 1,000,000,000 / 1,000 = 1,000,000
- So this expression equals 10⁶
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