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3 years ago

Simplify (8c^4w^2)^2 show work

Mathematics

1 answer:

muminat3 years ago

7 0

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.

$\displaystyle\left(8c^{4}w^{2}\right)^{2}=8^{2}\cdot c^{4\cdot 2}\cdot w^{2\cdot 2}\\\\=64c^{8}w^{4}$

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