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Questions and Answers
Evaluate the power of $4^3$.
64
Evaluate the power of $5^3$.
125
Evaluate the power of $(-7)^6$.
117649
Evaluate the power of $(-4)^5$.
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Write $11 imes 11 imes 11 imes 11 imes 11$ in exponential form.
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Write $3 imes 3 imes 3 imes 3 imes 3 imes 3 imes 3 imes 3$ in exponential form.
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Write $2 imes 2 imes 2$ in exponential form.
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Write $7 imes 7 imes 7 imes 7 imes 7$ in exponential form.
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Write $3 imes y imes y imes y$ in exponential form.
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Write $r imes r imes r imes r$ in exponential form.
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Write $(-5) imes (-5y) imes (-5y)$ in exponential form.
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Write $8$ as a repeated multiplication.
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Simplify $7^3 imes 7^2$.
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Simplify $5 imes 5^6$.
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Simplify $z^4 imes z^8$.
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Simplify $12^4 \ 12^3$.
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Simplify $2^4 \ 2^4$.
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Simplify $p^{12} \ p^8$.
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Study Notes
Exponents
- Definition: An exponent indicates how many times a base number is multiplied by itself.
- Base: The number being multiplied.
- Exponent: The small number written above and to the right of the base, indicating the number of times the base is multiplied by itself.
Rules of Exponents
- x⁰ = 1, x ≠ 0: Any number raised to the power of zero equals 1, except for zero itself.
- x¹ = x: Any number raised to the power of one is equal to itself.
- xᵐ × xⁿ = xᵐ⁺ⁿ: When multiplying exponents with the same base, add the powers.
- xᵐ ÷ xⁿ = xᵐ⁻ⁿ, x ≠ 0: When dividing exponents with the same base, subtract the powers.
- (xᵐ)ⁿ = xᵐ×ⁿ: When raising a power to another power, multiply the exponents.
- (xy)ᵐ = xᵐyᵐ: When raising a product to a power, apply the power to each factor.
- (x/y)ᵐ = xᵐ/yᵐ, y ≠ 0: When raising a quotient to a power, apply the power to both the numerator and the denominator.
- x⁻ᵐ = 1/xᵐ, x ≠ 0: A negative exponent indicates the reciprocal of the base raised to the positive value of the exponent.
Operations with Exponents
- Multiplication: Multiply the bases together and add the exponents if the bases are the same.
- Division: Divide the bases and subtract the exponents if the bases are the same.
- Raising to a power: Multiply the exponents together.
- Simplifying expressions: Use the rules of exponents to rewrite expressions in a simpler form.
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Description
This quiz covers the fundamental concepts of exponents, including definitions, base numbers, and specific exponent rules. Test your understanding of how to manipulate exponents through multiplication, division, and negative exponents. Perfect for students looking to solidify their knowledge in mathematics.
