Negative Exponents — Rules & Examples
Read this topicExplanations 3
- (Video) Negative Exponents by mathman1024 This video by mathman1024 defines negative exponents and explains how to simplify them. There are other exponent rules as well, includi…
By Alex Federspiel, Zora Gilbert, Victor Wang, Amy Feraco, Jonathan Heller, Joshua Siktar
- Raising a number to a negative power flips it on its head When you raise a number to a negative power, first raise the number to the absolute value of the power. The number we r…
By Zora Gilbert, Alex Federspiel, Amy Feraco, Joshua Siktar
- Negative Exponents Raising a number to a negative exponent isn't much different than raising a number to a positive exponent. The only difference is that a negative exponent mak…
By Alex Federspiel, Caroline K, Jonathan Heller, Joshua Siktar
Problems 46
- Rewrite without fractions: 2b−4−12a23a4.\frac{2}{b^{-4}} - \frac{12a^2}{3a^4}.b−42−3a412a2.
- What is 20175×2017−52017^5 \times 2017^{-5}20175×2017−5?
- True or False\text{True or False}True or False === If x≠0x\ne0x=0, then x5×x−10=x5x10x^5 \times x^{-10} = \frac{x^5}{x^{10}}x5×x−10=x10x5?
- True or False\text{True or False}True or False === 3−1=133^{-1} = \frac{1}{3}3−1=31?
- Is 22n2^{2n}22n, where nnn is any integer, always a natural number?
- Mark all pairs of like terms below.
- What is the value of (2)−3−(−4)−2(2)^{-3} - (-4)^{-2}(2)−3−(−4)−2?
- What is the value of the following expression? 24+232−2+2−3\frac{2^4 + 2^3}{2^{-2} + 2^{-3}}2−2+2−324+23
- Which of the following equals ax−4ax^{-4}ax−4, if a,x≠0a,x\ne0a,x=0?
- If x>1x>1x>1, find the value of nnn that satisfies x5×xn=1x^5\times x^{n}=1x5×xn=1
- If x>1x>1x>1, find the value of mmm that satisfies xm×x−4=1x^{m}\times x^{-4}=1xm×x−4=1
- If x>1x>1x>1, find the value of nnn that satisfies x2n−1×x−3=1x^{2n-1}\times x^{-3}=1x2n−1×x−3=1
- Find the value of 13−2\frac{1}{3^{-2}}3−21
- Find the value of 2−14−2\frac{2^{-1}}{4^{-2}}4−22−1
- Convert 1.32×10−31.32\times10^{-3}1.32×10−3 from scientific notation to decimal notation.
- Convert 4.13×10−24.13\times 10^{-2}4.13×10−2 from scientific notation to decimal notation.
- Simplify the following expression. x−3×y4x2×y−1\frac{x^{-3}\times y^4}{x^2\times y^{-1}}x2×y−1x−3×y4
- Simplify the following expression x−2×y−1x\frac{x^{-2}\times y^{-1}}{x}xx−2×y−1
- Simplify the following expression. x−1×y2x2×y−1\frac{x^{-1}\times y^{2}}{x^2\times y^{-1}}x2×y−1x−1×y2
- Simplify the following expression. (2x)−2×x(2x)^{-2}\times x(2x)−2×x
- Taking a number nnn to the power of −1-1−1 is the same as ...
- Simplify: (23)−1⋅(62)2\left(2^3\right)^{-1}\cdot\left(6^2\right)^2(23)−1⋅(62)2
- Write 0.1510.1510.151 in expanded notation.
- Calculate the following 2−62^{-6}2−6 and mark all answers below with the same value.
- Simplify (2)−2\left(2\right)^{-2}(2)−2 and (−2)−2\left(-2\right)^{-2}(−2)−2 \\ All answers are in respective order, choose the right one
- Simplify (2)−3\left(2\right)^{-3}(2)−3 and (−2)−3\left(-2\right)^{-3}(−2)−3 All answers are in respective order, choose the right one.
- Simplify (5)−1(5)^{-1}(5)−1
- Simplify the following: z×x−yz\times x^{-y}z×x−y Assume that x,y,z≠0x,y,z\neq{0}x,y,z=0
- What is 2−32^{-3}2−3?
- What is 2−42^{-4}2−4?
- What is 2−52^{-5}2−5?
- What is 3−23^{-2}3−2?
- What is 3−33^{-3}3−3?
- What is 3−43^{-4}3−4?
- What is 4−24^{-2}4−2?
- What is 4−34^{-3}4−3?
- What is 4−44^{-4}4−4?
- What is 5−25^{-2}5−2?
- What is 5−35^{-3}5−3?
- What is 6−26^{-2}6−2?
- What is 6−36^{-3}6−3?
- What is 7−27^{-2}7−2?
- What is (−2)−3(-2)^{-3}(−2)−3?
- Which is larger? AB2−1(12)−1\begin{array}{c|c} \text{A}&\text{B}\\ \hline 2^{-1}&\left(\frac12\right)^{-1} \end{array}A2−1B(21)−1
- Which is larger? AB3−14−1\begin{array}{c|c} \text{A}&\text{B}\\ \hline 3^{-1}&4^{-1} \end{array}A3−1B4−1
- Which is larger? AB(18)−1(19)−1\begin{array}{c|c} \text{A}&\text{B}\\ \hline \left(\frac18\right)^{-1}&\left(\frac19\right)^{-1} \end{array}A(81)−1B(91)−1