exponent operations

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the quotient of powers rule in exponent operations?
Back
The quotient of powers rule states that when dividing two expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n).
2.
FLASHCARD QUESTION
Front
How do you simplify the expression \( \frac{10p^4}{6p} \)?
Back
To simplify \( \frac{10p^4}{6p} \), divide the coefficients (10/6 = 5/3) and subtract the exponents of p (4-1 = 3), resulting in \( \frac{5p^3}{3} \).
3.
FLASHCARD QUESTION
Front
What is the product of powers rule in exponent operations?
Back
The product of powers rule states that when multiplying two expressions with the same base, you add the exponents: a^m * a^n = a^(m+n).
4.
FLASHCARD QUESTION
Front
How do you simplify the expression \( 7v^3 \cdot 10u^3v^5 \)?
Back
To simplify \( 7v^3 \cdot 10u^3v^5 \), multiply the coefficients (7*10 = 70) and add the exponents of v (3+5 = 8), resulting in \( 70u^3v^8 \).
5.
FLASHCARD QUESTION
Front
What is the power of a power rule in exponent operations?
Back
The power of a power rule states that when raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).
6.
FLASHCARD QUESTION
Front
How do you simplify the expression \( (3a^2)^2 \)?
Back
To simplify \( (3a^2)^2 \), square the coefficient (3^2 = 9) and multiply the exponents of a (2*2 = 4), resulting in \( 9a^4 \).
7.
FLASHCARD QUESTION
Front
What is the zero exponent rule in exponent operations?
Back
The zero exponent rule states that any non-zero base raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).
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