Exponent Quotient Rule — Definition & Examples
Read this topicExplanations 3
- (Video) Basic Exponent Properties by PatrickJMT Patrick JMT has a good video that explains the basic properties of exponents. Recall that an exponent is just a shorthand way of …
By Ben Ferrara, Alex Federspiel, Zora Gilbert, Amy Feraco, Jonathan Heller, Joshua Siktar
- (Video) Quotient Rule for Exponents by mathman1024 Here's a video by mathman1024 explaining the quotient rule for exponents. Summary\large{\text{Summary}}Summary The quotient ru…
By Alex Federspiel, Zora Gilbert, Amy Feraco, Caroline K, Joshua Siktar
- Quotient Rule for Exponents In order for the Quotient Rule for Exponents to work, the base in the numerator needs to be the same as the base in the denominator. You can't use th…
By Caroline K, Alex Federspiel, Joshua Siktar
Problems 57
- If h≠0h\ne0h=0, then h4h5=?\frac{h^4}{h^5} = ?h5h4=?
- Simplify z−2z4,\frac{z^{-2}}{z^4},z4z−2, if z≠0z\ne0z=0.
- True or False\text{True or False}True or False === If x≠0x\ne0x=0, then x5×x−10=x5x−10x^5 \times x^{-10} = \frac{x^5}{x^{-10}}x5×x−10=x−10x5?
- If l≠0l\ne0l=0 and l5÷l−3=ln{l^{5}}\div{l^{-3}} = l^nl5÷l−3=ln, find nnn.
- Simplify 318315.\frac{3^{18}}{3^{15}}.315318.
- Simplify 647618.\frac{6^{47}}{6^{18}}.618647.
- Simplify x15x78\frac{x^{15}}{x^{78}}x78x15 if x≠0x\ne0x=0.
- Let's define ⋄\diamond⋄ as follows: For any real numbers mmm and nnn, m⋄n=m5n3.m \diamond n = m^5n^3.m⋄n=m5n3. Knowing this, how can you simplify m⋄nn⋄m\frac{m \diamond n}{n \di…
- Simplify the following expression: x3y5xy2\frac{x^3y^5}{xy^2}xy2x3y5
- Simplify the following expression: x−2y10x5y3\frac{x^{-2}y^{10}}{x^5y^3}x5y3x−2y10
- Simplify the following expression if xxx is nonzero. x7x5+x10x−2\frac{x^{7}}{x^5}+\frac{x^{10}}{x^{-2}}x5x7+x−2x10
- Simplify the following expression when x≠0x\neq0x=0: x3x+x5x3\frac{x^{3}}{x}+\frac{x^{5}}{x^{3}}xx3+x3x5
- Simplify the following expression if xxx is nonzero. x6x7\frac{x^{6}}{x^7}x7x6
- Simplify the following expression if xxx is nonzero. x22x10+x15x7\frac{x^{22}}{x^{10}}+\frac{x^{15}}{x^{7}}x10x22+x7x15
- Simplify the following expression: x−5y7xy\frac{x^{-5}y^7}{xy}xyx−5y7
- Solve for the integer value of nnn: 2n23=25\frac{2^n}{2^3}=2^5232n=25
- Solve for the integer value of mmm: 25×272m×22=2\frac{2^5\times 2^7}{2^m\times 2^2}=22m×2225×27=2
- How do you divide powers with the same base?
- What is x4÷x3x^{4} \div x^{3}x4÷x3?
- What is x2÷x5x^{2} \div x^{5}x2÷x5?
- What is y6÷y2y^{6} \div y^{2}y6÷y2?
- What is x5x4\frac{x^{5}}{x^{4}}x4x5?
- What is x7x3\frac{x^7}{x^3}x3x7?
- What is x10÷x5x^{10} \div x^{5}x10÷x5?
- What is 24÷232^{4} \div 2^{3}24÷23?
- What is 36÷343^{6} \div 3^{4}36÷34?
- What is 47÷474^{7} \div 4^{7}47÷47?
- What is x5÷x7x^{5} \div x^{7}x5÷x7?
- What is 20162017÷201620162016^{2017} \div 2016^{2016}20162017÷20162016?
- What is y12÷y6y^{12} \div y^{6}y12÷y6?
- What is z4z2\frac{z^{4}}{z^2}z2z4?
- What is 162÷4216^{2} \div 4^2162÷42?
- Is (23)4÷(32)4(\frac{2}{3})^4\div(\frac{3}{2})^4(32)4÷(23)4 equal to (23)4÷(23)4(\frac{2}{3})^4\div(\frac{2}{3})^4(32)4÷(32)4? Choose the best answer.
- What is (23/421/2)\left(\frac{2^{3/4}}{2^{1/2}}\right)(21/223/4)?
- What is 11311−2\frac{11^3}{11^{-2}}11−2113?
- What is 4−443\frac{4^{-4}}{4^3}434−4?
- What is (23)3÷(32)5\left(\frac{2}{3}\right)^3\div\left(\frac{3}{2}\right)^5(32)3÷(23)5?
- Simplify the following: x4y−2x2y−3\frac{x^4 y^{-2}}{x^2 y^{-3}}x2y−3x4y−2
- What is nnn? a17×an=a16a^{17} \times a^n = a^{16}a17×an=a16
- Simplify the following: x5×x−2÷x3x^5\times x^{-2} \div x^{3}x5×x−2÷x3
- Simplify the following: 20x−55x4\frac{20x^{-5}}{5x^4}5x420x−5
- Simplify the following: 2x11÷x−62x^{11} \div x^{-6}2x11÷x−6
- Simplify the following: y102÷y26y46y^{102}\div \frac{y^{26}}{y^{46}}y102÷y46y26
- Simplify the following: x71÷x52÷x13x^{71} \div x^{52} \div x^{13}x71÷x52÷x13
- What is nnn? x−4÷xn=x2x^{-4} \div x^n = x^2x−4÷xn=x2
- Simplify the following: xx2÷x−3\frac{\sqrt{x}}{x^2}\div x^{-3}x2x÷x−3 Recall that x=x12\sqrt{x} = x^{\frac{1}{2}}x=x21.
- Using the method of subtracting integer exponents, simplify the following: 1x3÷x−2÷x−3÷x2x\frac{1}{x^{3}}\div x^{-2} \div x^{-3} \div \frac{x^2}{x}x31÷x−2÷x−3÷xx2
- What is nnn? x2÷x3÷x−1+yn÷y2=2x^2\div x^3 \div x^{-1} + y^n \div y^2 =2x2÷x3÷x−1+yn÷y2=2
- Simplify the following x−2+x3÷x5x^{-2} + x^3 \div x^{5}x−2+x3÷x5
- Simplify the following: x−2÷x0÷x−2x^{-2}\div x^0 \div x^{-2}x−2÷x0÷x−2
- Express bbb in terms of p,q,ap, q, ap,q,a given that: xp÷xq=xa⋅xbx^p \div x^q = x^a \cdot x^bxp÷xq=xa⋅xb
- Simplify the following: a7b8ca9b5c\frac{a^7 b^8 c}{a^9 b^5 c}a9b5ca7b8c
- Simplify the following: x11x10y\frac{x^{11}}{x^{10} y}x10yx11
- Simplify the following: x12x7\frac{x^{12}}{x^{7}}x7x12
- What is the relationship between the following expressions? x17x9,x15x7\frac{x^{17}}{x^9}, \frac{x^{15}}{x^7}x9x17,x7x15
- Simplify the following: x4x7÷x−3\frac{x^4}{x^7} \div x^{-3}x7x4÷x−3
- What is nnn? a6×an=a2a^6 \times a^n = a^{2}a6×an=a2