Podcast
Questions and Answers
Evaluate the power of $4^3$.
Evaluate the power of $4^3$.
64
Evaluate the power of $5^3$.
Evaluate the power of $5^3$.
125
Evaluate the power of $(-7)^6$.
Evaluate the power of $(-7)^6$.
117649
Evaluate the power of $(-4)^5$.
Evaluate the power of $(-4)^5$.
Write $11 imes 11 imes 11 imes 11 imes 11$ in exponential form.
Write $11 imes 11 imes 11 imes 11 imes 11$ in exponential form.
Write $3 imes 3 imes 3 imes 3 imes 3 imes 3 imes 3 imes 3$ in exponential form.
Write $3 imes 3 imes 3 imes 3 imes 3 imes 3 imes 3 imes 3$ in exponential form.
Write $2 imes 2 imes 2$ in exponential form.
Write $2 imes 2 imes 2$ in exponential form.
Write $7 imes 7 imes 7 imes 7 imes 7$ in exponential form.
Write $7 imes 7 imes 7 imes 7 imes 7$ in exponential form.
Write $3 imes y imes y imes y$ in exponential form.
Write $3 imes y imes y imes y$ in exponential form.
Write $r imes r imes r imes r$ in exponential form.
Write $r imes r imes r imes r$ in exponential form.
Write $(-5) imes (-5y) imes (-5y)$ in exponential form.
Write $(-5) imes (-5y) imes (-5y)$ in exponential form.
Write $8$ as a repeated multiplication.
Write $8$ as a repeated multiplication.
Simplify $7^3 imes 7^2$.
Simplify $7^3 imes 7^2$.
Simplify $5 imes 5^6$.
Simplify $5 imes 5^6$.
Simplify $z^4 imes z^8$.
Simplify $z^4 imes z^8$.
Simplify $12^4 \ 12^3$.
Simplify $12^4 \ 12^3$.
Simplify $2^4 \ 2^4$.
Simplify $2^4 \ 2^4$.
Simplify $p^{12} \ p^8$.
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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