Exponents And Scientific Notation

Product & Quotient

100

Product Rule: aⁿ + a^m= a^n+m

Question: 2³ * 2⁴

2³⁺⁴

=2⁷

⁼128

200

Quotient Rule: aⁿ/a^m= a^n-m

Question: 2^-7/ 2^-4

=2^-7--4

⁼2^-7+4

=2^-3

= 1/2³

=1/8

300

Quotient Rule: aⁿ/a^m= a^n-m

Question: u³/u⁵

=u^3-5

⁼u^-2

=1/u²

400

Product Rule: aⁿ + a^m= a^n+m

Question: 7^-5* 7⁵

=7^-5+5

=7⁰

=1

500

Quotient Rule: aⁿ/a^m= a^n-m

Question: 4¹¹/4⁵

=4^11-5

=4⁶

Power of a Fraction

100

Power Of A Fraction Rule: (a/b)^x = a^x/b^x

Question: (3/4)³

=3³/4³

⁼27/64

200

Power Of A Fraction Rule: (a/b)^x = a^x/b^x

Question: (2/7)²

=2²/7²

=4/49

300

Power Of A Fraction Rule: (a/b)^x = a^x/b^x

Question: (6/7)²

=6²/7²

=36/49

400

Power Of A Fraction Rule: (a/b)^x = a^x/b^x

Question: (3x/4y)⁴

=3⁴x⁴/4⁴y⁴

=81x⁴/256y⁴

500

Power Of A Fraction Rule: (a/b)^x = a^x/b^x

Question: (4x³/5t²)²

=4²x⁶/5²t⁴

=16x⁶/25t⁴

Negative Exponent

100

Negative Exponent: a^-x= 1/a^x

Question: x^-8

=1/x⁸

200

Negative Exponent: a^-x= 1/a^x

Question: 4^-5

=1/4⁵

300

Negative Exponent: a^-x= 1/a^x

Question: y^-2

=1/y²

400

Negative Exponent: a^-x= 1/a^x

Question: 7^-6

=1/7⁶

500

Negative Exponent: a^-x= 1/a^x

Question: 8^-5

=1/8⁵

Power Rule and Power of a Product

100

Power Rule: (bⁿ)^m = b^n*m 

Question: (x⁵)⁷

=X^5*7

=X³⁵

200

Power of a Product Rule: (ab)^x = a^x b^x

Question: (3v)⁴

=3⁴ v⁴

=81v⁴

300

Power of a Product Rule: (ab)^x = a^x b^x

Question: (6r)³

=6³r³

=216r³

400

Power of a Product Rule: (ab)^x = a^x b^x

Question: (7k⁴)²

=7²k^4*6

⁼49k²⁴

500

Power of a Product Rule: (ab)^x = a^x b^x

Question: (5²p³)²

=5^2*2p^3*2

=5⁴p⁶

=625p⁶

Zero Exponent

100

Zero Exponent: a⁰= 1

Question: 7⁰

=7⁰

=1

200

Zero Exponent: a⁰= 1

Question: 3⁰

=3⁰

=1

300

Zero Exponent: a⁰= 1

Question: cd⁰

=cd⁰

=c1

=c

400

Zero Exponent: a⁰= 1

Question: (2x⁵/4y²)⁰

=2⁰x^5*0/4⁰y^2*0

=1/1

=1

500

Zero Exponent: a⁰= 1

Question: (3f²f³/5g²)⁰

=3⁰f^2*0f^3*0/5⁰g^2*0
=1/1

=1