Card 1 of 20
EasyStudy card 1
Prompt
When multiplying powers with the same base, what happens to the exponents?
Answer
Add them.
Formula
\[a^m a^n=a^{m+n}\]
Example
\(x^4x^7=x^{11}\)
MathChapter 10: Law of Exponents and Polynomials
Flashcards
Laws of Exponents and Scientific Notation Flashcards
Twenty concise cards covering exponent structures, base conditions, reciprocals, conversions, operations, normalization, and common traps.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
When raising a power to another power, what happens to the exponents?
Answer
Multiply them.
Formula
\[(a^m)^n=a^{mn}\]
Example
\((y^3)^5=y^{15}\)
Card 3 of 20
EasyStudy card 3
Prompt
How does a power distribute across a product?
Answer
Raise every factor to that power.
Formula
\[(ab)^m=a^mb^m\]
Example
\((2xy)^3=8x^3y^3\)
Card 4 of 20
EasyStudy card 4
Prompt
What is the quotient-of-powers law for a nonzero base?
Answer
Subtract the denominator exponent from the numerator exponent.
Formula
\[\frac{a^m}{a^n}=a^{m-n}\]
Card 5 of 20
EasyStudy card 5
Prompt
What is \(a^0\) when \(a\ne0\)?
Answer
\(1\)
Card 6 of 20
EasyStudy card 6
Prompt
What does \(a^{-n}\) mean when \(a\ne0\)?
Answer
\(\frac{1}{a^n}\)
Formula
\[a^{-n}=\frac1{a^n}\]
Card 7 of 20
EasyStudy card 7
Prompt
Does a negative exponent make the value negative?
Answer
No. It indicates a reciprocal; the base determines the value's sign.
Card 8 of 20
MediumStudy card 8
Prompt
How do you simplify \((\frac{a}{b})^{-n}\)?
Answer
Take the reciprocal, then apply the positive power.
Formula
\[\left(\frac ab\right)^{-n}=\left(\frac ba\right)^n\]
Card 9 of 20
MediumStudy card 9
Prompt
Why do zero and negative exponent laws require a nonzero base?
Answer
Their quotient or reciprocal reasoning would otherwise create division by zero.
Card 10 of 20
MediumStudy card 10
Prompt
Can \(x^2+x^5\) be simplified to \(x^7\)?
Answer
No. The product law applies to multiplication, not addition.
Card 11 of 20
EasyStudy card 11
Prompt
What is normalized scientific notation?
Answer
\(a\times10^n\), where \(n\) is an integer and \(1\le|a|<10\).
Formula
\[a\times10^n,\quad1\le|a|<10\]
Card 12 of 20
EasyStudy card 12
Prompt
What exponent sign usually represents a large decimal number in scientific notation?
Answer
A positive exponent.
Example
\(620000=6.2\times10^5\)
Card 13 of 20
EasyStudy card 13
Prompt
What exponent sign usually represents a small nonzero decimal?
Answer
A negative exponent.
Example
\(0.0048=4.8\times10^{-3}\)
Card 14 of 20
MediumStudy card 14
Prompt
Convert \(7.1\times10^{-4}\) to decimal form.
Answer
\(0.00071\)
Card 15 of 20
MediumStudy card 15
Prompt
Write \(0.000039\) in scientific notation.
Answer
\(3.9\times10^{-5}\)
Card 16 of 20
MediumStudy card 16
Prompt
How are powers of ten combined when multiplying scientific-notation values?
Answer
Add their exponents.
Example
\(10^6\cdot10^{-2}=10^4\)
Card 17 of 20
MediumStudy card 17
Prompt
How are powers of ten combined when dividing scientific-notation values?
Answer
Subtract the denominator exponent.
Example
\(10^8/10^3=10^5\)
Card 18 of 20
MediumStudy card 18
Prompt
Normalize \(35\times10^4\).
Changing 35 to 3.5 divides the coefficient by 10.
Answer
\(3.5\times10^5\)
Card 19 of 20
HardStudy card 19
Prompt
Simplify \(\frac{x^9}{x^{12}}\) using positive exponents.
Answer
\(\frac1{x^3}\), for \(x\ne0\).
Card 20 of 20
MediumStudy card 20
Prompt
What final check should follow a scientific-notation calculation?
Answer
Confirm the coefficient satisfies \(1\le|a|<10\) and the scale matches the original value.
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