Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Express your answer using a single exponent. \newline(10c4)2(10c^4)^2

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Powers of a power: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using a single exponent. \newline(10c4)2(10c^4)^2
  1. Apply power rule: Apply the power of a power rule to (10c4)2(10c^4)^2. The power of a power rule states that (am)n=am∗n(a^m)^n = a^{m*n}. We will apply this rule to both the numerical part and the variable part of the expression. (10c4)2=(102)×(c4)2(10c^4)^2 = (10^2) \times (c^4)^2
  2. Calculate square of 1010: Calculate the square of 1010. \newline102=10×10=10010^2 = 10 \times 10 = 100
  3. Apply power rule to c4c^4: Apply the power of a power rule to c4c^4 raised to the power of 22. \newline(c4)2=c(4∗2)=c8(c^4)^2 = c^{(4*2)} = c^8
  4. Combine results: Combine the results from Step 22 and Step 33.\newline(10c4)2=100⋅c8(10c^4)^2 = 100 \cdot c^8

More problems from Powers of a power: variable bases

Question
Write the expression using an exponent.\newline2×22 \times 2\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Evaluate the expression. 4−42 4 - 4^2 ____
Get tutor helpright-arrow

Posted 9 months ago

Question
x2=4x^2 = 4
Get tutor helpright-arrow

Posted 7 months ago

Question
x2=9x^2 = 9
Get tutor helpright-arrow

Posted 10 months ago

Question
Solve for x. \newlinex2=0x^2 = 0 \newlineWrite your answer in simplified, rationalized form. \newlinex=x = _____ or x=x = _____
Get tutor helpright-arrow

Posted 10 months ago

Question
Solve for xx. \newline8=2x8 = 2^x \newline x=x = _____
Get tutor helpright-arrow

Posted 10 months ago

Question
Solve for xx. \newline6=7x6 = 7^x \newline x=x = _____
Get tutor helpright-arrow

Posted 10 months ago

Question
Select the equivalent expression.\newline((8−5)/(2−2))−4=?((8^{-5})/(2^{-2}))^{-4}=?\newlineChoose 11 answer:\newline(A) \newline(820)/(28)(8^{20})/(2^{8})\newline(B) \newline(26)/(89)(2^{6})/(8^{9})\newline(C) \newline(1)/(8⋅22)(1)/(8\cdot 2^{2})
Get tutor helpright-arrow

Posted 6 months ago

Question
Select the equivalent expression.\newline(b745)−3= ?\left(\frac{b^{7}}{4^{5}}\right)^{-3}=\,?\newlineChoose 11 answer:\newline(A) b21415\frac{b^{21}}{4^{15}}\newline(B) 415b21\frac{4^{15}}{b^{21}}\newline(C) b−21⋅4−15b^{-21}\cdot 4^{-15}
Get tutor helpright-arrow

Posted 8 months ago

Question
Select the equivalent expression.\newline(33⋅66)−3=(3^{3}\cdot6^{6})^{-3}=?\newlineChoose 11 answer:\newline(A) 139⋅618\frac{1}{3^{9}\cdot6^{18}}\newline(B) 61839\frac{6^{18}}{3^{9}}\newline(C) 39618\frac{3^{9}}{6^{18}}
Get tutor helpright-arrow

Posted 8 months ago

View all (90)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant