Zero (0) Exponent Rule — Definition & Examples
Read this topicExplanations 3
- Determining The Zero Exponent In mathematics, you try to make everything as consistent as possible. If a function works for positive numbers, how might it work for negative numb…
By Ivan Hu, Zora Gilbert, Alex Federspiel, Jonathan Heller, Joshua Siktar
- (Video) Quotient Properties and Negative Exponents by ThinkwellVids This video by ThinkwellVids explains what the theory behind numbers raised to a power of 000. Summary\large{\…
By Alex Federspiel, Zora Gilbert, Amy Feraco, Jonathan Heller, Joshua Siktar
- Zero Exponent Rule In other words, if you raise a nonzero number to the power of 0,0,0, the result is 1.1.1. Mathematicians debate the value of 00.0^0.00. Some say it's 1,1,1, a…
By Caroline K, Alex Federspiel, Joshua Siktar
Problems 36
- Does 10=20=30=n01^0 = 2^0 = 3^0 = n^010=20=30=n0 when n≠0n \neq 0n=0?
- What is x0×y0x^0\times y^0x0×y0, if x,y≠0x,y\ne0x,y=0?
- What is x0×(x−1)x^0 \times(x-1)x0×(x−1) when x≠0x\neq0x=0?
- If x≠0x \ne 0x=0, what is x0×25x^0 \times 25x0×25?
- If x>1x>1x>1, find an integer nnn such that 2000×xn=2000.2000\times x^n = 2000.2000×xn=2000.
- Simplify (13)0.\left(\frac{1}{3}\right)^0.(31)0.
- Simplify x0x^0x0 if x≠0x\ne 0x=0.
- Simplify (xy0)0(xy^0)^0(xy0)0 if x,y≠0x,y\ne0x,y=0.
- Simplify 3⋅403\cdot4^03⋅40.
- If x>1x>1x>1, find the value of nnn that satisfies 10xn=1010x^{n}=1010xn=10
- 21×2x=22^1\times2^x=221×2x=2 Solve for xxx.
- 2x2+x−6=12^{x^2+x-6}=12x2+x−6=1 Select all values of xxx that satisfy the equation. (Hint: You can check if a value of xxx works by plugging in the value.)
- 3x2−1=13^{x^2-1}=13x2−1=1 Select all values of xxx that satisfy the equation. (Hint: You can check if a value of xxx works by plugging in the value.)
- 23+2x−1=92^3+2^{x-1}=923+2x−1=9 Solve for xxx.
- Evaluate: (2x4y2z245x3)0\left(\frac{2x^4y^2z^2}{45x^3}\right)^0(45x32x4y2z2)0 if x≠0,y≠0,z≠0x \neq 0, y \neq 0, z \neq 0x=0,y=0,z=0
- Evaluate: (444)0(4^{4^{4}})^0(444)0
- Select the option with the least absolute value.
- Evaluate: 90×39^0 \times 390×3
- Evaluate: 20+20+202^{0} + 2^{0} + 2^{0}20+20+20
- Evaluate, then express in simplest form: 1+6030+60\frac{1+6^0}{3^0+6^0}30+601+60
- Evaluate: 4×504 \times 5^04×50
- Evaluate: 1234567890123456789^01234567890
- Complete the following statement: For any integer aaa, such that a>0a>0a>0, a0=?a^0=?a0=?
- Evaluate. (6x−3952u2353523−33400)0\left(\frac{6^x-395^{2u}}{23^{53523}-\sqrt[400]{33}}\right)^0(2353523−400336x−3952u)0
- 3−53×93×33^{-\frac53}\times \sqrt[3]{9} \times 33−35×39×3
- (1252)040\frac{\left(125^2\right)^0}{4^0}40(1252)0
- Which of the above expressions are equivalent?
- 11−84?112=111^{-\frac{8}{4}}\boxed{?}11^2=111−48?112=1 What is ?
- 1105311^05^311053 Evaluate
- What is xxx?
- 23424320÷234\frac{234^2}{432^0}\div23443202342÷234 Evaluate.
- Simplify the following: x3⋅x−2⋅x−1x^3\cdot x^{-2}\cdot x^{-1}x3⋅x−2⋅x−1
- Simplify the following: x2⋅x−5⋅x3+y1⋅y−1⋅y0x^2 \cdot x^{-5}\cdot x^3 +y^1\cdot y^{-1}\cdot y^0x2⋅x−5⋅x3+y1⋅y−1⋅y0 if x≠0,y≠0.x\neq 0, y\neq 0.x=0,y=0.
- Simplify the following if a≠0a\neq 0a=0: an⋅a2⋅a−n−1⋅a0a^{n} \cdot a^{2} \cdot a^{-n-1}\cdot a^0an⋅a2⋅a−n−1⋅a0
- Solve for nnn if x≠0x \neq 0x=0: x2n⋅x−1=1x^{2n}\cdot x^{-1} = 1x2n⋅x−1=1
- Evaluate. (10)0\left(\frac{1}{0}\right)^0(01)0