Exponent Product Rule — Definition & Examples
Read this topicExplanations 3
- (Video) Product Rule for Exponents by mathman1024 Here's a video by mathman1024 explaining the product rule. Summary\large{\text{Summary}}Summary The product rule for exponents …
By Alex Federspiel, Zora Gilbert, Amy Feraco, Caroline K, Joshua Siktar, Jonathan Heller
- Adding Exponents Let's be honest—exponents are little tiny numbers that can cause enormous headaches if you don't know how to handle them. The good news is that there are a few …
By Hannah Bonville, Zora Gilbert, Alex Federspiel, Amy Feraco, Jonathan Heller, Caroline K
- (Video) Basic Exponent Properties by PatrickJMT This video by PatrickJMT explains the basic properties of exponents. Recall that an exponent is just a shorthand way of referring…
By Ben Ferrara, Jonathan Heller, Alex Federspiel, Caroline K, Joshua Siktar
Problems 63
- f4×f−2=?f^4 \times f^{-2} = ?f4×f−2=?
- What is s3⋅s3s^3\cdot s^3s3⋅s3?
- What is 2t4⋅t82t^4\cdot t^82t4⋅t8?
- What is x3⋅y5x^3\cdot y^5x3⋅y5?
- What is b⋅b3⋅b−2b\cdot b^3\cdot b^{-2}b⋅b3⋅b−2, if b≠0b\ne0b=0?
- What is l6⋅l−10l^6\cdot l^{-10}l6⋅l−10, if l≠0l\ne0l=0?
- What is q3⋅q−3q^3\cdot q^{-3}q3⋅q−3 if q≠0q\ne0q=0?
- True or False\text{True or False}True or False === When you multiply powers with the same base, xxx, and the same exponent, aaa, the result will be x2ax^{2a}x2a.
- What is p102⋅−(4p)2p^{102}\cdot -(4p)^2p102⋅−(4p)2?
- Find x2×x5x^2 \times x^5x2×x5.
- If x52×x10=xnx^{5^2} \times x^{10} = x^nx52×x10=xn, find nnn.
- Which are true?
- If x20×x100=xnx^{20} \times x^{100} = x^nx20×x100=xn for some positive integer nnn, find nnn.
- If x52×x52=xnx^{5^2} \times x^{5^2} = x^nx52×x52=xn, find nnn.
- If x≠0x\ne0x=0 and x10×x−5=xnx^{10} \times x^{-5} = x^nx10×x−5=xn, find nnn.
- If x−5×x−100=xnx^{-5} \times x^{-100} = x^nx−5×x−100=xn for all x≠0x\ne0x=0, find nnn.
- Simplify the expression 57×59.5^7\times 5^9.57×59.
- Say you have a rectangular prism with width w=x2w = x^2w=x2, length l=x3l = x^3l=x3, and height h=x4h = x^4h=x4, for some real number xxx. What is its volume? (Hint: The volume …
- Simplify 1000(1000)10001000(1000)^{1000}1000(1000)1000.
- Select all that are correct.
- Simplify 23×25.2^3\times 2^5.23×25.
- Simplify 2×26×22.2\times 2^6\times 2^2.2×26×22.
- Simplify 23×24×2.2^3\times 2^4\times 2.23×24×2.
- Simplify x3×y4×y2.x^3\times y^4\times y^2.x3×y4×y2.
- Simplify x3×x−1.x^3\times x^{-1}.x3×x−1.
- Simplify x−5×x−3×x2.x^{-5}\times x^{-3}\times x^{2}.x−5×x−3×x2.
- Simplify 2−1×26×2−2.2^{-1}\times 2^6\times 2^{-2}.2−1×26×2−2.
- Simplify 2×2−1×220.2\times 2^{-1}\times 2^{20}.2×2−1×220.
- Simplify x3×x4×y−3×y−4.x^3\times x^4\times y^{-3}\times y^{-4}.x3×x4×y−3×y−4.
- 2p×23=262^p\times 2^3 = 2^62p×23=26 Find ppp.
- 36×3p=3−23^6\times 3^{p} = 3^{-2}36×3p=3−2 Find ppp.
- Select the possible values of xxx. x3×x6=x9x^3\times x^6=x^9x3×x6=x9
- Compute xn×xnx^n\times x^nxn×xn.
- Simplify the expression x7×x9.x^7\times x^9.x7×x9.
- How do you multiply powers with the same base?
- What is x2×xx^{2} \times xx2×x?
- What is y4×y7y^{4} \times y^{7}y4×y7?
- What is x12×x2x^{\frac{1}{2}} \times x^{2}x21×x2?
- What is x3×x2x^{3} \times x^{2}x3×x2?
- What is x4×xx^{4} \times xx4×x?
- What is x6×x3x^{6} \times x^{3}x6×x3?
- What is x23×x12x^{\frac{2}{3}} \times x^{\frac{1}{2}}x32×x21?
- What is x3×x3x^{3} \times x^{3}x3×x3?
- What is y6×y9y^{6} \times y^{9}y6×y9?
- What is y2z×yz2y^{2}z \times yz^{2}y2z×yz2?
- What is x5×x3x^{5} \times x^{3}x5×x3?
- What is z2×z4z^{2} \times z^{4}z2×z4?
- What is x14×x18x^{\frac{1}{4}} \times x^{\frac{1}{8}}x41×x81?
- Simplify the following. x3⋅x0⋅n5⋅n−1x^3\cdot x^0\cdot n^5\cdot n^{-1}x3⋅x0⋅n5⋅n−1
- What is 23×22^3\times 223×2?
- What is 3−1×(−3)53^{-1}\times (-3)^{5}3−1×(−3)5?
- What is 5−3×545^{-3}\times 5^45−3×54?
- What is 2353×22542^35^3 \times 2^25^42353×2254?
- Can you apply the product rule to 1325×2335\frac{1}{3}^{\frac{2}{5}}\times \frac{2}{3}^{\frac{3}{5}}3152×3253?
- Solve for xxx: 4250(−8)6x>(−2)5254^{250}(-8)^{6}x > (-2)^{525}4250(−8)6x>(−2)525
- Simplify the following: b2×a2×a−1×a5×b3b^2 \times a^2 \times a^{-1} \times a^5 \times b^3b2×a2×a−1×a5×b3
- What is nnn? a(2+3)×a2×3=ana^{(2+3)} \times a^{2\times 3} = a^na(2+3)×a2×3=an
- Simplify the following: a2×b2a^2 \times b^2a2×b2
- What is nnn? x5⋅xn=x−3x^5 \cdot x^n = x^{-3}x5⋅xn=x−3
- Simplify the following: x−5⋅x3⋅x−4x^{-5}\cdot x^3 \cdot x^{-4}x−5⋅x3⋅x−4
- Simplify the following: (x2⋅x⋅x10)+(x3⋅x6⋅x)(x^2\cdot x\cdot x^{10}) + (x^3\cdot x^6 \cdot x)(x2⋅x⋅x10)+(x3⋅x6⋅x)
- Simplify the following equation: (x⋅x5⋅x2)+(x3⋅x⋅x4)(x\cdot x^5 \cdot x^2) +(x^3 \cdot x\cdot x^4)(x⋅x5⋅x2)+(x3⋅x⋅x4)
- Simplify the following: x2⋅x2⋅x2x^2\cdot x^2 \cdot x^2x2⋅x2⋅x2