Answer:
2x^7
Step-by-step explanation:
Multiply
x
^4 by x
^3 by adding the exponents.
Answer:
b = ![\frac{7}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B12%7D)
Step-by-step explanation:
b +
= 1
← change to an improper fraction
b +
= ![\frac{5}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D)
Multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions
12b + 8 = 15 ( subtract 8 from both sides )
12b = 7 ( divide both sides by 12 )
b = ![\frac{7}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B12%7D)
Exponents are not particularly mysterious. They show repeated multiplication. That is ...
... c⁴ = c·c·c·c
... w² = w·w
Then the factor inside parentheses is ...
... 8·c·c·c·c·w·w
The exponent outside parentheses tells you the number of times this is repeated as a factor:
... (8c⁴w²)² = (8·c·c·c·c·w·w)(8·c·c·c·c·w·w)
... = 8·8·c·c·c·c·c·c·c·c·w·w·w·w = 64c⁸w⁴
_____
You can take advantage of the fact that multiplication is repeated addition, so the exponents of the various factors can be found by multiplying the outside exponent by the inside exponents.
![\displaystyle\left(8c^{4}w^{2}\right)^{2}=8^{2}\cdot c^{4\cdot 2}\cdot w^{2\cdot 2}\\\\=64c^{8}w^{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cleft%288c%5E%7B4%7Dw%5E%7B2%7D%5Cright%29%5E%7B2%7D%3D8%5E%7B2%7D%5Ccdot%20c%5E%7B4%5Ccdot%202%7D%5Ccdot%20w%5E%7B2%5Ccdot%202%7D%5C%5C%5C%5C%3D64c%5E%7B8%7Dw%5E%7B4%7D)