10 Questions
What is the result of (2^3 × 2^4)?
2^7
Simplify the expression (3^2)^4.
3^8
What is the result of (2^3 × 3^3)^2?
2^6 × 3^6
Simplify the expression 2^5 ÷ 2^3.
2^2
What is the value of a^(-2) in terms of a?
1/a^2
What is the result of (a^3 b^2)^4?
a^12 b^8
What is the result of a^5 × a^(-3)?
a^2
What is the result of (a^2 b^3) × (a^4 b^2)?
a^6 b^5
What is the result of a^3 ÷ a^(-2)?
a^5
What is the result of (a^2)^3 × (a^3)^2?
a^13
Study Notes
Exponent Laws
Product of Powers
-
Law:
a^m × a^n = a^(m+n) - When multiplying two exponential expressions with the same base, add the exponents
Power of a Power
-
Law:
(a^m)^n = a^(mn) - When raising an exponential expression to a power, multiply the exponents
Power of a Product
-
Law:
(ab)^m = a^m × b^m - When raising a product of two bases to a power, raise each base to that power and multiply
Quotient of Powers
-
Law:
a^m ÷ a^n = a^(m-n) - When dividing two exponential expressions with the same base, subtract the exponents
Zero Exponent
-
Law:
a^0 = 1 - Any base raised to the power of 0 is equal to 1
Negative Exponent
-
Law:
a^(-n) = 1/a^n - A negative exponent is equivalent to the reciprocal of the positive exponent
Test your understanding of the exponent laws, including the product of powers, power of a power, power of a product, quotient of powers, zero exponent, and negative exponent. Practice applying these laws to simplify exponential expressions and solve problems.
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